form form (basis of approximating space)
norm norm (criteria of approximation, figure of merit, nonstandard data)
var variable (coordinate transform, mesh generation)
diag diagnostics
tools tools from other fields
omit omitted topics
geometry geometry of the domain or graph
data nonstandard data
crease discontinuities (jump, crease, edges)
expdesign experimental design
coord coordinate transformation
selection selection of regression variables
vparam choice of parameterization variable
iso isoparametric finite elements
mesh mesh generation, refinement
file-format file format
simplemesh simple spline mesh utilities
optinterp ``optimal'' spline interpolation (particular choice of knots)
segment segmented piecewise linear approximation
stopping stopping criteria for grid points
triang triangulation, given scattered points
adaptive adaptive grids
meshgen multivariate mesh generation
b78s de Boor 78 INTERV, L2KNTS
dasl DASL/B1KE, B1KPE
port Schryer PORT/UMB, LUMB, PUMB, IMMM, MNPB
imsl imsl/bsnak not-a-knot condition
stop/plateau plateau in $||r||$
stop/autocorr $\mathop{\rm autocorr}(r)\le{1 / \sqrt{2(N-1)}}$
GCV cross-validation
stop/ML maximum likelihood
b78s de Boor 78 Practical Guide, page 266
p70smoo Powell 70
g87gcv Girard 87 estimate trace using residual for random normal data
dg91gcv Deshpande Girard 91 robust and Poisson norm
GCV1 univariate
GCV2 bivariate
w75cv Wahba 75 spline smoothing
o85cv O'Sullivan 85 O(n) GCV smoothing spline
h86cv deHoog Hutchinson 86 O(n) GCV smoothing spline
w86cv Woltring 86 GCV smoothing spline
hh87orth deHoog Hutchinson 87 replaces Cholesky by orthogonal linear algebra
ka87smoo Kohn Ansley 87 filtering
su88gcv Schumaker Utreras 88 complete spline (endpoint deriv data)
blwy86 Bates Lindstrom Wahba Yandell 86 gcvpack
y87block Yandell 87 e.g. disconnected regions but single smoothing parameter
b83ml Brannigan 83 Approx Thy IV
bf85sph Baumgardner Frederickson 85 uniform triangulation on sphere
voronoi Delaunay-Thiessen (dual to Voronoi polygons); max-min angle
other-tri other (data-independent) triangulation criteria
data-tri data dependent triangulation
searchtri searching general triangulation for given point
nonconvex-tri dealing with nonconvex domains
minmaxtri min-max angle
w92minmax Waupotitsch 92 Tan edge insertion
dlr90tri Dynb Levin Rippa 90 allow thin triangles near steep fronts
qs91tri Quak Schumaker 91 diagonal flip starting from uniform grid
s93tri Schumaker 93 simulated annealing on l2 error; local swaps does about as well
obs92voronoi Okabe Boots Sugihara 92 monograph on Voronoi, Delaunay
voronoi2d bivariate
voronoi3d three and more
l77c1 Lawson 77 swap diagonal in quadrilaterals to max the min angle
a78toms Akima 78 bivariate interpolation
cr84tri Cline Renka 84 adjacency list
bl84 Barnhill Little 84 min the max angle
f86sweep Fortune 86 sweep in transformed space
f91triang Fortune 91 survey
etw92tri Edelsbrunner Tan Waupotitsch 92 max angle
b81vor Bowyer 81
w81cont Watson 81
j89del Joe 89
l77c1 Lawson 77 step to neighbor triangle in right direction
s87tri Schumaker 87 lexicographic sorting; may need N^2 space
pt88tri Preparata Tamassia 88
sp92solidsolid Sapidis Perucchio 92 deciding if cells are in or out
refine refinement
unrefinement unrefinement
freeknot free knots
freeknot0 free knots for piecewise constant
freeknot2 free grid in more than one variable
jitter nonuniform sampling to ameliorate aliasing
quasirandom quasirandom (more uniform than true random would be)
adlm90rem Arge Daehlen Lyche Morken 90 Constrained Knot Removal
hddhjmss94 Hoppe et al 94 linear patches to control points and creases
m87nonunif Mitchell 87 Poisson disk; adaptive sampling; multistage averaging
s84go Schagen 84 tradeoff between sampling entire space and resolving minima
f86quasi Fox 86 Faure, Halton, Sobol sequences (evenly distributed over square)
cutbig refine intervals with large residual
cuttri refine triangle
cutcrit refine using critical features
segment segmented piecewise linear approximation
kd k-d tree
hier hierarchical rectangular grid
subdiv recursive subdivision
d87fit Dierckx 87 curfit, smoot
cj87l1 Cox Jones 87 drop redundant knots
af88refine Adjerid Flaherty 88
m89refine Mitchell 89 comparison of linear triangle refinements
hg95scape Heckbert Garland 95 greedy insertion
scds91tri Schmitt Chen Du Sair 91 Gregory-Bezier triangle
sp90tri Scarlatos Pavlidis 90 put triangle edges along ridgelines
h66seg Hudson 66
ph74seg Pavlidis Horowitz 74 split-and-merge piecewise linear
w76seg Wilson 76 greedy-algorithm piecewise linear
p77polyg Pavlidis 77 Newton's method starting from split-and-merge
wd84polyg Wall Danielsson 84 fast merging
dt90curv Dudek Tsotsos 90 look for jumps in curvature
mw92arc Meek Walton 92 circular arc
h93polyg Hobby 93 boxes around given vertices
h96polyg Hobby 96 fast good visible vertices
r78adapt Rice 78 ADAPT (assumes f, f' available)
br79mult de Boor Rice 79 multivariate with optimal convergence
d80refin Dahmen 80 multivariate splines
bsw83datastr Bank Sherman Weiser 83 data structures for refinement
hierbasis hierarchical basis
quadtree quadtree, octree
rectcover rectangular covering
wavelet wavelet, quadrature mirror filter
y85hier Yserentant 85 include both "broad" and "narrow" elements in basis
a92hier Anderson 92 combining local approximations, then distributing effects
gm84wavelet Grossman Morlet 84 wavelet, also known as multiresolution
bcr89wavelet Beylkin Coifman Rokhlin 89
v90wavelet Vavasis 90 piecewise constant on refined triangles
m91wave Micchelli 91 prewavelet
c92wave Chui 92
ys83quadtree Yerry Shephard 83 quadtree, boundary adjustment, smoothing
b86rot Berger 86 clustering; rotated rectangles
g87mov Gropp 87 moving hierarchical grids
br90clust Berger Riugoutsos 90 covering by oriented rectangles
f79cart Friedman 79 piecewise constant on k-d tree
r85kd Rosenberg 85 comparison of quad and kd trees
cdg88 Cleveland Devlin Grosse 88 loess k-d trees, blending
g89loess Grosse 89 further details
f88mars Friedman 89 MARS (extreme) subsample of tensor product spline basis
e88strat Eubank 88 tridiagonal Newton, asymptotic, statistical applications
br68free de Boor Rice 68 optimize one knot at a time
p70smoo Powell 70
j78free Jupp 78 nonlinear l2 after log transform
bs79free Barrow Smith 79
nss86seg Nurnberger Sommer Strauss 86 allows jumps at knots
n86free Nurnberger 86 pp-segment; fix knots and use Remez
newnot de Boor newnot
free-ode methods applied to differential equations
d91free D'Azevedo 91 adaptive triangles for simple geometry and functions
b74newnot de Boor 74 newnot
s86ssaf Schryer 86 driver for newnot
imsl imsl/bsvls newnot driver for least squares data fitting
p89newnot Pryce 89 newnot iteration
ps75pasva Pereyra Sewell 75
w79free White 79 coordinate transformation
kn80mesh Kautsky Nichols 80 bounding local mesh ratio
cd85mesh Carey Dinh 85 coordinate transformation
amr88bvp Ascher Mattheij Russell 88 survey in chapter 9
b78s de Boor 78 SPLOPT
imsl imsl/bsopk
g78range Gaffney 78 given bound on high deriv, what possible function?
t90range Thakur 90 specialized to second derivative bound
mw81des Micchelli Wahba 81
b83leb Bos 83
chebpt sample at Chebyshev points $\cos{j\pi\over n}$
fr88fejer Fischer Reichel 88 updatable, approximately Fejer distributions
statdesign optimal statistical design
blendpt blending
hr87sub Hoffman Reddy 87 subset of uniform points near Chebyshev set
bd87design Box Draper 87 bias v. variance, checking fit, factorial designs
f90design Faraway 90 local
$f''^{2/9}$hs91design Hardin Sloane 91 pattern search
g69lattice Gordon 69 distributive lattices
dps78ser Delvos Posdorf Schempp 78 adds a few points in interior of cells
twm85grid Thompson Warsi Mastin 85 grid generation by PDEs
j86triang Joe 86 filling convex polygons with triangles
femhand Shepard Abel 87 chapter 5.3.4, 5.4.3b
bgr88obtuse Baker Grosse Rafferty 88 nonobtuse triangulation
be91triang Bern Eppstein 91 survey
kw92atlas Kalik Wendland 92 p.l.triangulation of differential manifold
mf92plate McMahon Franke 92 choose Voronoi regions for scattered data
r92tri Ruppert 92 iterative Delaunay, adding circumcenter to skinny triangles
bdy-struct boundary data structures
cs77byu Christiansen Stephenson 77 MOVIE.BYU
cg89tensor Coughran Grosse 89 scatter data or rectangular mesh
llmmpds90 Lounsbery Loop Mann Meyers Painter DeRose Sloan 90 dstruct
p90format Pratt 90 CAD data exchange standards
w85bdy Weiler 85 winged edge
w85bdyc Woo 85
w88bdy Wilson 88
a92bdy Ala 92 "delta" E->F, F->V, V->E; paging off disk
timeser time series, digital filters, signal processing
intersect finding intersections
minimal minimal surfaces
quadrature quadrature
fn special functions
extrap extrapolation, acceleration of series
dsp79 IEEE DSP
b85filter Bose 85 digital filters
w86time Wilson 86
jt87time Jones Tryon 87 unequally spaced data
bg82gmsolid Boyse Gilchrist 82 GMSolid CSG to boundary representation
d85inters Dokken 85
hefs85inters Houghton et al 85
g85resolv Goldman 85 resolvents
ck87inters Chandru Kochar 87 intersection by elimination
ch89impl Chuang Hoffmann 89
nsk90clip Nishita Sederberg Kakimoto 90 Bezier clipping
m91intersect Mullenheim 91
m91intersect2 Mullenheim 91
bl86min Barbosa Lucas 86
gw69 Golub Welsch 69 Gaussian rule from eigensystem
dr84i Davis Rabinowitz 84 Methods
bl84quad Barnhill Little 84 cut long side of triangle with max error
h68ca Hart et al 80 Computer Approximations
cw80e Cody Waite 80 Elementary Functions
c87s Cody 87
fnlib fnlib
f80fn Fullerton 80 Bibliography
t89exp Tang 89 exp (small table, like traditional software)
elliptic elliptic integrals, Jacobian elliptic functions
t92expm1 Tang 89 exp(x)-1
bs92bessel Boisvert Saunders 92 vfnlib
fl67ellip Fair Luke 67 incomplete elliptic integrals by Pade
c79ellip Carlson 79 incomplete elliptic integrals 1-,2-,3-kind
bdg81 Bjorstad Dahlquist Grosse 81
b82neville Brezinski 82 Muhlback-Neville-Aitken Havie E-algorithm
sfs86MMPE Sidi Ford Smith 86 "modified minimal polynomial extrapolation"
k81 Knuth 81 generators, test, shuffling
m85rand Marsaglia 85 update on Fibonacci, combinational generators; tests
f86quasi Fox 86 Faure, Halton, Sobol sequences (evenly distributed over square)
gz85rand Guralnik Zemach 85 uniform random in and on a sphere, on a Cray XMP
a88rand Altman 85 more testing
a90rand Anderson 90 vectorization
p93rand Petersen 93 buffer tricks
t77eda Tukey Exploratory Data Analysis
w79free White 79 equidistributing mesh
twm85grid Thompson Warsi Mastin 85
bf85ace Breiman Friedman 85 estimating transformations for regresson
scaling scaling, centering, sphere-ing, decorrelation
conformal conformal mapping
polar polar coordinates
tt81 Tukey Tukey 81 automatic decorrelation
agk82 Art Gnanadesikan Kettenring 82 estimating within-cluster covariance matrix
t80sc Trefethen 80 Schwarz-Christoffel
h86conf Henrici 86 conformal mapping up to 86
bg87arc Bjorstad Grosse 87 circular arc polygons
d86polar Dierckx 86 tensor spline on circle
f88mars Friedman 89 MARS
stepwise stepwise
subsets all subsets
m73Cp Mallows 73 $C_p$ plots (option in imsl/rbest)
fw74leap Furnival Wilson 74 leaps and bounds
g79sweep Goodnight 79 forward stepwise regression
h77subset Hocking 77
ak82subset Armstrong Kung 82
polyrat polynomial, rational
sfem spline, finite element
specific other specific approximating spaces
refine grid refinement
techniques techniques for combining specific methods
param parametric, geometric/visual continuity
abstract abstract spaces
poly real polynomial
rational real rational
complex complex polynomial, rational
polyzero zeros of polynomials
w71zero Wilkinson 71
m73zero Madsen Reid 73 PA06,7
j75zero Jenkins 75
crease discontinuities (jump, crease, edges)
spline splines
fem finite elements
trig trigonometric
specfun special functions (approximation by, not approximation of)
kernel kernel smoothing
moving moving least squares
radial radial basis functions
wavelet wavelet, quadrature mirror filter
Urysohn Urysohn's lemma
cm89 Cavendish Marin 89 blend between domains specified by offset curves
cm89 Cavendish Marin 89 blend between domains specified by offset curves
s90surv Sabin 90 comprehensive survey
fs90hodo Farouki Sakkalis 90 polynomial arclength, rational offset
knotins knot insertion for splines
km83sub Koparkar Mudur 83 subdivision at algebraic points
dlg87 Dyn Levin Gregory 87 interpolatory
mp87sub Micchelli Prautzsch 87
h86box Hollig 86 recursive subdivision of box splines
s91subdiv Sabin 91
bounds bounds
directrix directrix, correspondence, and generator
multi1 extension of univariate methods to multivariate
stage multistage methods
iso isoparametric approximation ($\min_{P,Q}\|f\circ P-Q\|$)
GC generalized cone
offset offset
fillet fillets
s90surv Sabin 90 comprehensive survey
a91devel Aumann 91 suff conditions for developable Bezier patch
nb77gc Nevatia Binford 77 space curve and cross-section function
u-der univariate
estder/l2 least squares local quadratic
estder/dir weighted average of directional derivatives
estder/var variational method (minimize integral of derivatives)
a85estder Alfeld 85 minimum energy over piecewise polynomials
network minimum norm network
a70jacm Akima 70 local average of slopes
em77local Ellis McLain 77
iky77sweep Ichida Kiyono 77
a91der Akima 91 improved accuracy over Akima 70
l77c1 Lawson 77 software for $C^1$
a78toms Akima 78 bivariate interpolation
m80scat Mansfield 80 weighted average of directional derivatives
a84der Akima 84 weighted average of directional derivatives
bl84 Barnhill Little 84 triangular Shepard
a96der Akima 96 [tensor] weight cubic estimates by deviation from l2 line
a96der2 Akima 96 [scatter] weight cubic estimates by deviation from l2 plane
hh87blending Hoffmann Hopcroft 86 projective blending surfaces
w86fillet Warren 86 algebraic surfaces as fillets
p87l2alg Pratt 87 product of base surface and "truncating surface"
ro87blending Rockwood Owen 87 "super elliptic blend"
s90surv Sabin 90 comprehensive survey; trimming
Haar Haar system
genfun generating function methods (generalized Pad\'e)
linalg general linear basis functions
opt general non-linear basis functions
alg-eq implicit algebraic equations
dif-eq differential equations
functional functional approximation
power power
Newton Newton form of interpolating polynomial
Cheby Chebyshev
Bezier barycentric, Bernstein-Bezier curves and patches
poly/orth general orthogonal
polycon constrained
m-poly multivariate
powereval evaluation
polyint integrals
h68ca Hart et al. 68 Horner's rule and alternatives
f68eval Fike 68 economized methods
z83poly Ziv 83 factored form, more stable than Horner
s87tri Schumaker 87 raster evaluation
hpw90horner Hansen Patrick Wang 90 scaling to avoid overflow
s87tri Schumaker 87 bivariate integral over triangle
gr84interp Gasca Ramirez 84
egk87poly Egecioglu Gallopoulos Koc 87 parallel interpolation and evaluation
fr88fejer Fischer Reichel 88 updatable, approximately Fejer distributions
Cheby-interp interpolation to function and derivative data
Cheby-l2 least squares
Cheby-eval evaluation
Cheby-deriv derivatives
Cheby-int integrals
Cheby-diag/std standard errors from least squares fit
Cheby-con endpoint constrained
k70poly Krogh 70 polynomial interpolation; E01AEF
T1FE Cox 86 Clenshaw Forsythe least squares fitting
fnlib Fullerton 81 CSEVL
port Warner 75 TCHBP
dasl DASL/T1VE
bs92bessel Boisvert Saunders 92 vectorization
dasl DASL/T1DE
dasl DASL/T1QE
dasl DASL/T1SE
l88cheb Lachance 88 degree lowering for curves and surfaces
f57orth Forsythe 57 generate polynomials given abscissa
w59orth Weisfeld 59 extension of Householder Stiefel to several variables
port Warner 75 ORTHP evaluation, given recurrence coefficients
s75poly Shampine 75 advocates double precision residual
cb80 Conte de Boor 80 least squares polynomial fitting
tl81 Ting Luke 81 conversion between different bases
g82orth Gautschi 82 recurrence coefficients for general weights
poly/orth/add adding and deleting points
poly/orth/sob Sobolev norm
d77l2 Davidon 77 ``online'' algorithm
egk89 Elhay Golub Kautsky 89 rotations, Lanczos
ikns88 Iserles Koch Norsett SanzSerna 88
ch65 Clenshaw Hayes 65; T1FCE
mo86polycon Mason Opfer 86 discretized infinite program; Newton on dual
kt89 Kaufman Taylor 89 linear constraints on coefficients and range
m-poly/eval evaluation
m-poly/approx approximation, interpolation
cg90horner Carnicer Gasca 90 Horner graph
cy77interp Chung Yao 77 geometric conditions for interpolation
gr84interp Gasca Ramirez 84
b85interp Busch 85
bj85orth Bartels Jezioranski 85 Forsythe-style orthogonal basis
d87hex Dunkl 87 orthogonal polynomials on the hexagon
m88multi Muhlbach 88 generalized polynomial interpolation on tensor grid
kt89 Kaufman Taylor 89
p90c1c2 Preusser 90 C^2 9th-degree triangle for 4th-order vertex Hermite data
Remez Remez exchange
diffcor differential correction
linequality linear inequality method
ratinterp interpolation
pade Pad\'e
ratpow power of polynomial in denominator
t86cf Trefethen 86 Caratheodory-Fejer
kt88inf Kaufman Taylor 88 infinite interval
st89cf Saff Totik 89 polynomial Caratheodory-Fejer fails
mc90rat Manocha Canny 90 polynomial parametrizations
d93param Degen 93 eighth-order rational cubic
pgy93l2 Pratt Goult Ye 93 orthog poly, SVD
m63remez Maehly 63 exchange zeros rather than extrema
m67 Meinardus 67 section 7.1
b87remez Breuer 87 Thiele interpolation and secant iteration
remez1 Remez, first (single exchange)
remez2 Remez, second (multiple exchange)
c76remez Chalmers 76 linear constraints, e.g. monotone polynomials
jf87remez Jing Fam 87
d80remez Dunham 80 user supplies functions and derivatives
ns83remez Nurnberger Sommer 83 splines
co66 Curtis Osborne 66
s76li Simpson 76 polynomial
c86aa Cheney 86 Algorithms for Approximation
bcl87lp Bartels Conn Li 87
c88remez Chiang 88 modification for degeneracy
port Eldredge Warner 76 PORT/BURAM,BURM1
klt78 Kaufman Leeming Taylor 78 combined Remez - differential correction
c86aa Cheney 86 Algorithms for Approximation
lr73rat Lee Roberts 73
d84rat Dunham 84 for nearly optimal results, need high precision
g81rat Graves-Morris 81 reordering points before interpolation
bh81rat Graves-Morris Hopkins 81 continued fraction; E01RAF
c87rat Cuyt 87 recursion for multivariate rational, compared with others
cw87rat Cuyt Wuytack 87 inverse, reciprocal, qd, Gradd, eps, Stoer
c88rat Cuyt 88 convergent of a multivariate continued fraction
bb92rat Barel Bultheel 92
baryrat barycentric
b88rat Berrut 88 coefficients of equal size, no poles
b89sinc Berrut 89 stable form of sinc series without sin evaluations
harwell Morgan 64 PE06
m81pade Mason 81
cw87rat Cuyt Wuytack 87 continued fraction, qd, Gragg, determinant, Viscovatov, recursive, eps, multivariate
tg87cp Trefethen Gutknecht 87 like Pad\'e, but match Chebyshev series
c78ratpow Carta 78 take root, linearize, iterate
d87ratpow Dunham 87 Remez
fixed-cr known, fixed crease
free-cr unknown crease, to be found
brz76fault Bolondi Rocca Zanoletti 76 slit in thin plate
fn83disc Franke Nielson 83 adding jumps and creases to Shepard surfaces
s85edge Shiau 85 many methods
dt90curv Dudek Tsotsos 90 look for jumps in curvature
h92discont Hechbert 92 put triangle edges where jumps can be predicted
ms85edge Mumford Shah 86 min (length+gradient+L2) by Euler-Lagrange
s85edge Shiau 85 many methods
m86persmoo McDonald 86 ``split linear fit'' left, center, and right
c86edge Canny 86 numerical optimization for filter; multiscale
tp86edge Torre Poggio 86 regularization, zero-crossing; comparative remarks
b87edge Bergholm 87 multiresolution
lph88disc Lee Pavlidis Huang 88
l88edge Lee 88
g90edge Girard 90 global spline with free jumps
hddhjmss94 Hoppe et al 94 linear patches to control points and creases
c86edge Canny 86 edge dectection
b87edge Bergholm 87 edge dectection
gkm91bnd Gopalsamy Khandekar Mudur 91 optimal sample and Lebesque constant
c92ratsubdiv Cheng 92 perspective correction in estimating subdivision level
u-spline univariate
m-spline multivariate
pl piecewise linear
pch pch: piecewise cubic Hermite
pp pp: general piecewise polynomial
B-spline B-splines
Bezier Bernstein-Bezier curves
spline-conv conversion between different bases
s-spline specialized splines
adaptive free knots
b78s de Boor 78 BSPLPP,BSPP2D B-spline to truncated power, imsl/bscpp
f86wfb Fritsch 86 any $G^1$ cubic can be reparameterized as $C^1$
h87conv Hoschek 87 higher degree, fewer Bezier pieces <-> lower, more
gf87r2t Goldman Filip 87 cut rectangle along diagonal
f88rep Fritsch 88 converting $G^2$ cubic to B-spline with double knots
t92remov Tiller 92 power -> Bezier -> B-spline, then remove redundant knots
ss86rat Sakai Silanes 86
elastica elastica
nu-spline $\nu$, $\beta$, $\gamma$, Manning, Farin, W-F
tension taut splines, splines under tension
network minimum norm network spline
weighted-spline weighted splines
s-spline-other other
s84w2nd Salkauskas 84 interpolation and piecewise constant weight
f87wnu Foley 87 interval and point tension by weighted nu-splines
kl90qspline Kulkarni Laurent 90 inverse piecewise linear weights
s83hyper Schumaker 83 recursion
al68spline Anselone Laurent 68 linear system for general linear functionals
catmull-rom Catmull-Rom
d-spline discrete spline
EHB-spline EHB-spline (unusual smoothness constraints)
spec-spline spectral spline
conic-spline conic spline
bern-spline Bernoulli spline
s91bern Stockler 91 multivariate Bernoulli spline
p83conic Pavlidis 83
p85conic Pratt 85
p89conic Pham Binh 89 tridiagonal system
acctab tabulate at arguments where values need few digits
segment breakpoint placement
g85tab Gal 85 table based method for highly accurate functions
acgsst86 Agarwal et al. 86
t89exp Tang 89 exp (small table, like traditional software)
m90tab Markstein 90 rounding issues
gb91tab Gal Bachelis 91 exp, log, trig for IEEE
z91tab Ziv 91 use higher precision when first approximation isn't decisive
fn84pchip Fritsch 82 monotone interpolation, evaluation
f88monol2 Fritsch 88 least squares
u-der derivative estimation
nss86seg Nurnberger Sommer Strauss 86 allows jumps at knots
nearsmooth almost smooth (jumps less than $\epsilon$)
pp-eval evaluation of general piecewise polynomial
pp-onepass one-pass least squares fitting
b78s de Boor 78 PPVALU
imsl imsl/ppval,ppder,ppitg
y87onepass Yoshimoto 87 fit data on interval and two neighbors
b78s de Boor 78 Practical Guide
B-spline-fit fitting, interpolation
B-spline-eval evaluation, derivatives, integral
B-spline-zero zeros
knotins subdivision, knot insertion
degraise degree raising
B-diag diagnostics, error estimation
ratBspl rational B-splines
B-interp interpolation
endcond end conditions for interpolation
B-local local, variation diminishing
B-quasi quasi-interpolation
B-l2 least squares fitting
B-l1 $l_1$ fitting to data points
B-li $l_\infty$ fitting to a function
b78s de Boor 78 CUBSPL, SPLINT, SPLI2D
dasl DASL/B1IE, B1IPE
imsl imsl/bsint
optinterp ``optimal'' spline interpolation
B-many many-knot interpolation
dgm88many Dahmen Goodman Micchelli 88
ls75local Lyche Schumaker 75 anything that reproduces polynomials
dgm88many Dahmen Goodman Micchelli 88
b78s de Boor 78 QUASI (chapter XII, example 4)
s85ppf Sablonniere 85 quasi-interp on 3-direction mesh
cl87box Chui Lai 87 quasi-interp box spline
B-l2d fitting discrete data
B-l2f fitting user function
b78s de Boor 78 L2APPR
dasl DASL/B1FE, B1FPE
imsl imsl/bslsq
port Schryer PORT/DL2SF
port Schryer PORT/L2SFF
cj87l1 Cox Jones 87 spline l1 fitting, shape preserving
n86free Nurnberger 86 pp-segment; then fix knots and use Remez
b86remez Blatter 86 adaptation of Remez to splines
l74end Lucas 74 higher order accurate derivatives
bc88end Beatson Chacko 88 end $f'$ of cubic interpolant
Bs-eval spline evaluation
B-eval B-spline basis evaluation
Bs-deriv spline derivatives
B-deriv B-spline basis derivatives
Bs-int spline integrals
B-int B-spline basis integrals
Bs-fourier Fourier transform
knotins knot insertion and degree raising
b78s de Boor 78 BVALUE (BVALU2 has right endpoint continuous from left)
dasl DASL/B1VE, B1VPE
imsl imsl/bsval
port Schryer PORT/SPLNE
l86bse Lee 86 comparison of Lee and Boehm speedups
swf91eval Silbermann Wang Ferrari 91 speedup of forward differencing
b78s de Boor 78 BSPLVB
port Schryer PORT/BSPLE
b78s de Boor 78 BVALUE
dasl DASL/B1DE, B1DPE
imsl imsl/bsder
port Schryer PORT/SPLND, SPLN1
b78s de Boor 78 BSPLVD
port Schryer PORT/BSPLD, BSPL1
dasl DASL/B1QE, B1QPE, B1SQE, B1SQPE
imsl imsl/bsitg
port Schryer PORT/SPLNI
g76int Gaffney 76
port Schryer PORT/BSPLI
vbh92quad Vermeulen Bartels Heppler 92 integral of B-spline * function
g72atten Gautschi 72 attenuation factors
g80per Gutknecht 80 conjugate function
n81four Neuman 81 arbitrary knots
g87per Gutknecht 87 attenuation factors for tensor and box splines
d87per Delvos 87
d87fit Dierckx 87 sproot (cubics only)
g89zero Grandine 89 interval Newton
B-diag/std standard errors from least squares fit
B-diag/fun function and spline
B-diag/dat two splines
dasl DASL/B1SE, B1SPE, (derivatives) B1SDE, B1SDPE
port Schryer PORT/EESFF, EESFI
port Schryer PORT/EEBSF
deglower degree lowering
h82essen Henrici 82 section 5.4.e, with flowchart for equal-step case
gm83bern Gonska Meier 83 comprehensive bibliography
f90cs Farin 90 evaluation by nested multiplication, p.48
f90cs Farin 90 degree raising, p.64
s87g1pat Sarraga 87 $G^1$ Bezier patch interpolating Bezier curves
sv86tri Schumaker Volk 86 evaluating Bernstein Bezier polynomial on triangle
s87tri Schumaker 87 evaluating Bernstein Bezier polynomial on triangle
s90triB Seidel 90 generalized Bezier patch using polar forms
cr74 Catmull Rom 74
bg88cr Barry Goldman 88
d80dspl Duris 80 Lyche cubic discrete spline oslo
oslo Cohen Lyche Riesenfeld 80 Oslo algorithm for subdivision
b80ins Boehm 80 knot insertion
lr80sub Lane Riesenfeld 80 subdivision
bp85 Boehm Prautzsch 85 inserting a knot sequence
d86subdiv Dahmen 86 subdivision
bpa87sub Boehm Prautzsch Arner 87 Bezier, subdivision of triangular spline
lm87deg Lyche Morken 87 fit spline of one degree and knots by another
deglower degree lowering
p84deg Prautzsch 84
cls85deg Cohen Lyche Schumaker 85 degree raising for splines
lm87deg Lyche Morken 87 fit spline of one degree and knots by another
ch91lower Cox Harris 91 left-to-right greedy algorithm
h87conv Hoschek 87 higher degree, fewer Bezier pieces <-> lower, more
e93lower Eck 93 variat of Forrest 72
pt87ratB Piegl Tiller 87
l87conic Lee 87 relationship with conics
s73spl Spaeth 73 tension varies from interval to interval
c74tension Cline 74
b78s de Boor 78 TAUTSP adds knots to cubic rather than using exponential basis
r80tension Rentrop 80
nf84tension Nielson Franke 84 minimum norm network spline with tension
r87tension Renka 87 choice of tension parameters for shape preservation
sk88tension Sapidis Kaklis 88 convex, monotone
kl91tension Koch Lyche 91 Bezier form
r93tension Renka 93 interpolating or smoothing, with bounds constraints
n74nu Nielson 74 $\nu$-spline
f86wfb Fritsch 86 any $G^1$ cubic can be reparameterized as $C^1$
h86mock Hobby 86 approximately $G^2$
f87wnu Foley 87 interval and point tension by weighted nu-splines
f88rep Fritsch 88 converting $G^2$ cubic to B-spline with double knots
f88wnu Foley 88 montone, convex constrained variational problem
lf73elas Lee Forsythe 73 definitions
m73n Malcolm 73 Nonlinear splines
r81nbb K-D Reinsch 81 Munchen PhD thesis
gj82e Golomb Jerome 82 global and local analysis of curvature functional
k86elastica Kallay 86 given endpoint locations and directions, total length
bn88elastica Bruckstein Netravali 88 min length * energy
jh91elastica Jou Han 91
b92elastica Brunnett 92 param by max curvature, tension
e92elastica Edwards 92 nonlinear equation solver, elliptic integrals
js76ehb Jerome Schumaker 76 support basis construction
c78fem Ciarlet 78
modulef Begis Hecht Vidrascu 84
femhand Finite Element Handbook 87
fem2 bivariate
fem3 trivariate and general dimension
est+fem estimate nodal information for finite element
fem2/tri triangle
fem2/rect rectangle
iso isoparametric approximation ($\min_{P,Q}\|f\circ P-Q\|$)
param/irr irregular patches for otherwise rectangular grid
fem2/tri/quad quadratic, piecewise quadratic
fem2/tri/cub cubic, piecewise cubic
fem2/tri/quin {$C^1$} quintic, piecewise quintic
fem2/tri/rat rational
fem2/tri/other other
p74quad Powell 74 {$C^1$} quadratic triangle for contour plotting
ps77quad Powell Sabin 77 {$C^1$} quadratic triangle for contour plotting
st81quad Sibson Thomson 81 16-triangle rectangle with linear grad on edges
dvv92powellsabin Dierckx VanLeemput Vermeire 92 smoothing, least sq, adapt
g87c1l2 Gmelig Meyling 87 function and derivative at vertices and internal Bezier point
g87c1 Grandine 87 B-net min norm perturbation of piecewise linear, by SOR
clough-tocher Hsieh-Clough-Tocher {$C^1$} cubic macro-triangle
bb82shell Bernadou Boisserie 82 shell finite elements
p90c1c2 Preusser 90 C^1 quintic triangle for 2nd-order vertex Hermite data
m76rat McLain 76 local quadratic at vertices; distance to opposite side
b77surf Barnhill 77 Brown, Little rational triangle
m80scat Mansfield 80 {$C^1$} rational triangle (with Birkhoff 74)
w83rat Wang 83 $C^1$ rational
ab84tri Alfeld 84 $C^2$ cubic and quintic precision
h85tri Herron 85 $C^1$ rational; cubic precision
n80mn Nielson 80 minimum pseudonorm; 9-parameter $C^1$ element with linear normals
s81nn Sibson 81 Natural Neighbor Interpolation
p90c1c2 Preusser 90 C^2 9th-degree triangle for 4th-order vertex Hermite data
ct65 Clough Tocher 65 C1 cubic macro-triangle
bh81ct Bernadou Hassan 81 basis functions, complete and reduced
bb82shell Bernadou Boisserie 82 shell finite elements
m78curtri Mansfield 78 curved triangle
f85sct Farin 85 $C^2$ variant
wf87ctn Worsey Farin 87 n dimensional
m72 Melkes 72 reduced Hermite interpolation (zeros cross-product terms)
bpd80 Baszenski Posdorf Delvos 80 explicit Melkes; $C^2$-conforming
n86melkes Nienhaus 86 $C^1$-conforming
gh73trans Gordon Hall 73 blending functions
m78curtri Mansfield 78 curved triangle
fhp78iso Frey Hall Porsching 78 sufficient conditions
f83iso Field 83 invertible quadratic elements
c83iso Citipitioglu 83
tetrahedra tetrahedron
blendmult discretizations of blending on simplices
s91omega Sabin 91 20-node quad brick versus B-spline
a84tetr Alfeld 84 $C^1$ rational
a84tetrct Alfeld 84 quintic Clough-Tocher
wf87ctn Worsey Farin 87 n dimensional cubic Clough-Tocher
wp88tetr Worsey Piper 88 Powell-Sabin-type $C^1$-quadratic, 24 pieces
r88morley Ruas 88 gen. Morley's triangle; $C^0$-quadratic
h73insight Hamming 73 Numerical Methods
port Warner 75 TRIGP ``vector variation of Horner's rule''
gm87trig Giunta Murli 87 trig coefficients
FFT FFT
spectral spectral methods
b86hartley Bracewell 86 fast Hartley transform
dr92trig Dutt Rokhlin 92 approx by guassian*sin
clw70fft Cooley Lewis Welch 70 FFT with various symmetries
s69fft Singleton 69 complex and real in one or more variables
te73symm Ten Eyck 73 crystallographic FFT
dsp79 IEEE DSP
s82fft Swarztrauber 82 FFTPACK
s91fft Schoemake 91 efficient permutation
t92fft Temperton 92 roughly 1.25 faster than Cooley-Tukey
d93fft Dahlquist 93 logarithmic grid
go77spec Gottlieb Orszag 77
gt85local Gottlieb Tadmor 85 physical-space localization
chqz87 Canuto Hussaini Quarteroni Zang 87
exp sum of exponentials
gaus sum of gaussians
sinc sinc
varp VARPRO
h73insight Hamming 73 Numerical Methods
k79l1exp Kammler 79
r80exp Ruhe 80 discrete nonnegative least squares, then Prony
w87exp Watson 87 $l_1$
s88genfun Small 88 methods of Prony and of Tuttle
w90exp Watson 90 $l_\infty$
gp73varp Golub Pereyra 73
k75varp Kaufman 75 speedup of Golub Pereyra
kp78varp Kaufman Pereyra 78 nonlinear equality constraints
gl79varp Golub LeVeque 79 multiple sets of linear coeff for one set of nonlinear
port Gay Kaufman port/nsfb,nsf1 simple bound constraints; single nonlinear
s86go Schagen 86 Internal Modelling for Global Optimization
s81sinc Stenger 81
bers86sinc Butzer Engels Ries Stens 86 alternatives using splines
b89sinc Berrut 89 stable form of sinc series without sin evaluations
g85resolv Goldman 85 resolvents for implicitization
w86fillet Warren 86 algebraic surfaces as fillets
p87l2alg Pratt 87 best algebraic under geometric distance
s87implicit Sederberg 87 pictures
bhlh88implicit Bajaj Hoffmann Lynch Hopcroft 88
b90implicit Bajaj 90 $G^1$ interpolation
g91bdyelem Georg 91 integral of basic function projected onto manifold
kw92atlas Kalik Wendland 92 p.l.triangulation of differential manifold
wh94particle Witkin Heckbert 94 repelling particles on surface
quadric patches on quadric surfaces
cubic patches on cubic surfaces
implicit-approx approximation of parametric curve by implicit
param-approx approximation of implicit curve by parametric
paramdat data near parametric curve
wl90quad Warren Lodha 90 projective image of plane triangle under quadratic
dhj93quad Dietz Hoschek Juttler 93 Pythagorean quadruples in polynomial rings
lw92cubic Lodha Warren 92 rational biquadration Bezier; skew-line coordinates
p88implicit Patterson 88 parametric cubics as implicit curves
ch89impl Chuang Hoffmann 89
pgv91conic Potier Guermah Vercken 91 look for locally constant cross ratio
m91circle Morken 91 symmetric, $C^1$ quadratic approximation to circular arc
v82diffeq Varah 82 differential equations
d75ia Davis 75 basic definitions and examples
exp sum of exponentials
Remez Remez exchange
s88genfun Small 88
sn82compl Streit Nuttall 82
w88clin Watson 88 l-infinity complex linear system
w88compl Watson 88 l-infinity complex function
c/poly polynomial
c/rat rational
f81taylor Fornberg 81 numerical estimation of Taylor series
r84aorth Reichel 84 approximate Faber polynomials on Jordan curve
g86compl Gutknecht 86 best on domain by conformal mapping, projection
fr88fejer Fischer Reichel 88 updatable, approximately Fejer distributions
t88remez Tang 88 single-exchange Remez
r86lr Reichel 86 fix basis; interpolate at points on boundary
t86cf Trefethen 86 Caratheodory-Fejer
param/p parametric smoothness desired
param/g only geometric smoothness of locus of points needed
param/p1 curves
param/p2 surfaces
dasl (see also DASL spline routines with letter L)
param/g1 curves
param/g2 surfaces
bhs87 de Boor Hollig Sabin 87 $O(h^6)$ cubics
gu88g2 Goodman Unsworth 88 cubic segments and straight lines
nu-spline $\nu$, $\beta$, $\gamma$, Manning, Farin, Wilson-Fowler splines
s89param Schaback 89 convergence order of many methods
kl90qspline Kulkarni Laurent 90 $G^2$
l90vcquart Lasser 90 $VC^3$ and $VC^4$
s91univ Seidel 91 Bezier from spline, knot insertion for $G^1$
d93param Degen 93 eighth-order rational cubic
vparam choice of parameterization variable
p-spline spline
p-conic piecewise conic
tl2 orthogonal distance regression splines
ordering ordering scattered points
e76param Epstein 76 chordal distance is better than uniform
m83param Marin 83 minimize second derivative; better than chordal
f86wfb Fritsch 86 any $G^1$ cubic can be reparameterized as $C^1$
h88intrin Hoschek 88
l89param Lee 89 centripetal (sqrt chordal)
f90cs Farin 90 p.130-134
fs90hodo Farouki Sakkalis 90 polynomial arclength, rational offset
a91param Alt 91 conic on 3 points, various criteria
df91order Dedieu Favardin 91 fit algebraic by l2 and laplacian penalty
d87fit Dierckx 87 fitpack(parcur,clocur,concur), param
m83i McLaughlin 83 planar interpolation
f85mcl Frey 85 piecewise parabolic
mw92arc Meek Walton 92 similar to segmentation methods
h92arc Hoschek 92 shortest interpolating circular arc spline
csyl88 Choi Shin Yoon Lee 88 triangles from scattered data on surface
param/irr irregular patches for otherwise rectangular grid
s83tr Sabin 83 triangular and pentagonal patches
sb89nsided Storry Ball 89 C1 patch for bicubic neighbors
ld90nsided Loop DeRose 90 biquadratic, bicubic Sabin nets
p93box Peters 93 $C^1$ irregular cubic patch for mesh of Zwart patches
p95surf Peters 95 $C^1$ quadratic using corner cutting
f83surf Farin 83 variant of Clough-Tocher for parametric surfaces
j87assem Jensen 87 mixing triangles and rectangles
n87g1patch Nielson 87 a 6-parameter $G^1$ triangle
ss87patch Shirman Sequin 87 local, polynomial
scds91tri Schmitt Chen Du Sair 91 Gregory-Bezier triangle
r91cross Renner 91 twist compatibility and cross derivatives
c87fejer Clutton-Brock 87 kernels for sphere
shepard distance weighted interpolation (Shepard)
movingl2 (finite weight) least squares
s68irr Shepard 68 Two-dimensional interpolation for irregular-spaced data
gw78shep Gordon Wixon 78 Shepard's method
b77surf Barnhill 77 transfinite Shepard
fn80shep Franke Nielson 80
l83ccs Little 83 triangular Shepard
f86mls Farwig 86 interpolation by moving least squares
bpr87geod Barnhill Piper Rescorla 87 distance along geodesic
r88shep Renka 88 modified Shepard in 2 and 3 dimensions with k-d tree
m74contour McLain 74 distance weighted least squares onto rectangular mesh
c79lowess Cleveland 79 (univariate) lowess; n/2 near neighbors
ls86csf Lancaster Salkauskas 86 Curve and Surface Fitting; derivatives
m86persmoo McDonald 86 ``split linear fit'' left, center, and right
cdg88 Cleveland Devlin Grosse 88 (multivariate) loess; partial sort, k-d trees, blending
multiquad Hardy's multiquadrics
plate thin plate splines $r^2 \log r^2$
gaus sum of gaussians
radial/gen algorithms applicable to many radial bases
radial/other other
dl81bell Dyn Levin 81 bell-shaped bases for Hardy, thin plate
dlr86pcg Dyn Levin Rippa 86 iterated Laplacian as preconditioner
bl88neural Broomhead Lowe 88 interpretation as neural network
mf92plate McMahon Franke 92 choose Voronoi regions for scattered data
js91box Jetter Stoeckler 91
sw93l2radial Sivakumar Ward 93 theory for fixed set of centers
s80cont Sabin 69 tech report $r^3$ instead of $r^2 \log r^2$
gtensor tensor product and similar methods
blending blending, Coons patch, transfinite element
additive additive $f(x,y) \approx g(x)+h(y)$
nomographic nomographic $\approx f(u(x)+b(y))$, ACE
proj projection pursuit, $\approx \sum f(\alpha\cdot x)$
tensor rectangular grid data; tensor splines
ten/slice slices parallel to coordinate axis
ten/scat scattered data
ten/miss missing data
ten/cur curved mesh lines
ratprod rational product
ps73ten Pereyra Scherer 73
b79ten de Boor 79 tensor computations with a twist
ten-spline-fit fitting, interpolation
ten-spline-twist twist estimation
ten-spline-ev evaluation, derivatives
ten-interp interpolation
ten-l2 least squares fitting
ten-rank low rank
f90cs Farin 90 p.276-280,350
b78s de Boor 78 SPLI2D, imsl/bs2in,bs3in
dasl DASL/B2IRE, B2IPRE
wz88pl Weiser Zarantonello 86 piecewise linear interpolation in n dim
cj74ten Call Judd 74 least squares in n dimensions
h75ten Hartley 75 least squares in n dimensions
d77ten Dierckx 82 l2 cubic
g80ten Grosse 80 normal equations ok if in factored form
d81ten Dierckx 81 tensor smoothing for scattered data
dasl DASL/B2FRE, B2FPRE
d80rank Demko 80 $\sum_i f_i(x) g_i(y)$ using SVD
f88mars Friedman 89 MARS
ten-spline-eval evaluation
ten-spline-deriv derivatives
ten-spline-int integrals
dasl DASL/B2VRE, B2VPRE
imsl imsl/bs2vl,bs3vl
port Grosse PORT/VDSS1,VDSS2,VDSS3
dasl DASL/B2DXE, B2DYE, B2DPZE, B2DPTE
imsl imsl/bs2dr,bs3dr
imsl imsl/bs2ig,bs3ig
ch65 Clenshaw Hayes 65 least squares bivariate polynomial
dasl tensor spline DASL/B2FE
hh74bicub Hayes Halliday 74
$\Delta u = 0$
c87state Cox 87 Hayes curved knot lines planned for DASL
kt75rat Kaufman Taylor 75
h77ratprod Henry 77
blendrect rectangular patch
blendtri triangular patch
blendcur network of curves
recontour slices parallel to coordinate plane
Urysohn Urysohn's lemma
blendmult more than two variables
nat-ten boundary data as basis functions
blendpt experimental design
c75blend Cavendish 75 local mesh refinement
bbk78twist Barnhill Brown Klucewicz 78 alternatives to 0 cross derivatives
b77surf Barnhill 77 Gregory, Little and Brown squares
bs93bubble Bercovier Shilat 93 Coons patch plus bubble function from serendipity element
bbg73tri Barnhill Birkhoff Gordon 73 interpolate parallel to side
b77surf Barnhill 77
g78tri Gregory 78 symmetric rational and polynomial blending
n79sv Nielson 79 side-vertex radial projectors
n80mn Nielson 80 minimum pseudonorm
ab84tri Alfeld Barnhill 84 $C^2$ quintic blending
h86curv Hagen 86 blending value, derivative, and curvature
f86tripatch Foley 86 integrates on boundary (relatively expensive)
w78cur Wixom 78 data on collection of intersecting curves
jpw91blend Jensen Petersen Watkins 91 cross-boundary derivatives
fku77 Fuchs Kedem Uselton 77 reconstructing object from slices
b88cont Boissonnat 88 pruning Delaunay
kf88cont Kehtarnavaz Figueiredo 88 match segments by shape; blend
m76tetr Mansfield 76 tetrahedra
bl84 Barnhill Little 84 BBG and radial Nielson
a85perp Alfeld 85 general dimension, smoothness, precision
g85simp Gregory 85 simplex extension of triangle method
t76natten Thomas 76 error $10^-3$ better than cubic blending for $e^{x(1-y)}$, $N=4$
h82anova Hemmerle 82 analysis of variance
c86aa Cheney 86 Algorithms for Approximation
ht86add Hastie Tibshirani 86
oyr86add O'Sullivan Yandell Raynor 86
f88mars Friedman 89 MARS
w91add Wahba 91 r.k.H.s.
fgs83 Friedman Grosse Stuetzle 83 improved projection pursuit regression
t88stat Thisted 88 section 4.6.1
c86aa Cheney 86 Algorithms for Approximation
bf85ace Breiman Friedman 85 estimating transformations for regresson
h71m Hardy 71 J Geophys Res
f82t Franke 82 tests of scattered data interpolation
f87bihash Foley 86 Interpolation and approximation of scattered data
p91multi Powell 91 choice of parameter
bp92multi Beatson Powell 92 univariate quasi-interp
bp92end Beatson Powell 92 endpoint correction
m-pp pp: general piecewise polynomial
tensor tensor product splines
plate thin plate splines
simplex simplex splines
box box splines; uniform grid
triB triangular B-spline
irrspline irregular mesh spline
supspl super spline
network minimum norm network spline
m-spline-conv conversion between different bases; degree lowering
a88news Alfeld 88 Multivariate Spline Newsletter
g86c1cub Gmelig Meyling 86 $C^1$ cubic triangles by sparse linear $l_2$
Bezier Bernstein-Bezier patches
polyharmonic polyharmonic spline
b74thin Briggs 74
brz76fault Bolondi Rocca Zanoletti 76 slit in thin plate
f82thin Franke 82
f85tens Franke 85 with tension
l86toep Lee 86 conjugate gradients, block Toeplitz
blwy86 Bates Lindstrom Wahba Yandell 86 gcvpack
qs88thin Quak Schumaker 88 calculating energy for Bernstein-Bezier patch
uv91scat Utreras Varas 91 monotone thin plate spline for scattered data
ss91plate Sibson Stone 91 precondition by Dirichlet bdy/dist
g97thin Goodsell 97 multigrid for many observations on circle
r91polyhar Rabut 91
mru91polyhar Micchelli Rabut Utreras 91 subdivision
r92polyhar Rabut 92
r92polyhar2 Rabut 92 finer discretization of Laplacian than in r92polyhar
f71triB Frederickson 71
s90triB Seidel 90 generalized Bezier patch using polar forms
bpa87sub Boehym Prautzsch Arner 87 Bezier, subdivision of triangular spline
fs93simplex Fong Seidel 93 pictures of Dahmen Micchelli Seidel 92 construction
l94irrspline Loop 94 refine to deg 4 mesh; quad-net; quartic triangles
cl87supspl Chui Lai 87
s89supspl Schumaker 89 basis construction
dm81mbspl Dahmen Micchelli 82 l2
dm82mbspl Dahmen Micchelli 82
h82mbspl Hollig 82
g87simpl Grandine 87 pessimistic
g87knot Gmelig Meyling 87 choice of knots
g87l2 Gmelig Meyling 87 evaluation and least square fitting
g88simpl Grandine 88
s85ppf Sablonniere 85 $C^1$ quadratic on criss-cross
bpa87sub Boehym Prautzsch Arner 87 Bezier, subdivision of triangular spline
d87sub Dahmen 87 multivariate spline on uniform grid by subdivision
j87assem Jensen 87 box splines for parametric surfaces
g87per Gutknecht 87 attenuation factors for tensor and box splines
d88box Dahmen 88 truncated power basis
box/eval evaluation
box/interp interpolation and quasi-interpolation
h86box Hollig 86 recursive subdivision
c88mspl Chui 88 B-nets of box splines
l92box Lai 92 recurrence DxB(*|X)=B(*|X-x)-B(*-x|X-x) and deriv of Bezier
cl87box Chui Lai 87 quasi-interp box spline
cdr88 Chui Diamon Raphael 88
dl88 Daehlen Lyche 88
wz88pl Weiser Zarantonello 86 piecewise linear interpolation in n dim
js91box Jetter Stoeckler 91 submodule; attenuation factors
hsw89conv Hoschek Schneider Wassum 89 GC^1 bicubic, GC^2 biquintic
est+fem estimate nodal information for finite element
stage2 interpolate scattered data onto rectangular grid
boolean Boolean sum, other than blending
overlap smooth averaging of overlapping local patches
residfit iterated fitting of residual
GMDH Ivakhnenko GMDH
neural adaptive learning networks
fgs83 Friedman Grosse Stuetzle 83 projection pursuit regression
f84del Foley 84 delta sum BL + S(I-BL)
s85cont Sabin 85 dynamic addition
f84gmdh Farlow,ed. 84 "group method of data handling"
bl88neural Broomhead Lowe 88
triang triangulation
estder estimate values, derivatives (for use with finite element)
fem finite element
blending blending
s76surf Schumaker 76 Fitting surfaces to scattered data
bg75bool Barnhill Gregory 75 $P \oplus Q$ has interpolation of $P$ and precision of $Q$
b77surf Barnhill 77 Shepard $\oplus$ least squares
ls86csf Lancaster Salkauskas 86 Curve and Surface Fitting
m72interp Maude 72 Hermite cubic weight of local polynomials
jmj73 Junkins Miller Jancaitis 73 overlap weighting
f77interp Franke 77 weighted average of local interpolant at data points
u79cv Utreras 79 thin plate splines on overlapping subregions
f82thin Franke 82
d86cv Daman 86 weighted overlap better than global
ac87strip Anthony Cox 87 fit coarse grid line by strips; bdy cond for patch
n83mnn Nielson 83 Minimum Norm Network
nf84tension Nielson Franke 84 minimum norm network spline with tension
nr87sph Nielson Ramaraj 87 Interpolation over a sphere
mc89mtf Montefusco Casciola 89 Min Tension Functional, related to Nielson 80
tensor data on rectangular grid
nearten data on nearly rectangular grid
track data along tracks, possibly intersecting
infint infinite interval
sphere functions defined over the surface of a sphere
alg-eq functions defined over the surface of a manifold
branch branching curve; multivalued function
paramdat points lying near a parametric curve
projective projective space
s85cont Sabin 85 1) precondition by snapping to grid; 2) parametric
param/irr irregular patches for otherwise rectangular grid
e71track Ewen-Smith 71
blendcur blending on network of curves
kt88inf Kaufman Taylor 88 rational approximation on infinite interval
lp91proj Lee Phillips 91 lattices for interpolation
sph/ten tensor grid (latitude, longitude)
sph/utri uniform triangulation
sph/other scattered over sphere
csphere curves on the surface of a sphere in 3 or 4 dimensions
s79sph Swarztrauber 79 scalars
s81sph Swarztrauber 81 vectors
w84sph Wahba 84 cross validation
d84sph Dierckx 84 tensor smoothing spline, scattered data
d86sph Dierckx 86 spherical harmonic coefficients of bicubic spline
d87sph Dierckx 87 tensor smoothing spline, lat.-long. data
gmp87sph Gmelig Meylin Pfluger 87 reconstruction from cross sections
t87sph Traas 87 $C^1$ by tensor spline with spherical harmonics at poles
st91sph Schumaker Traas 91 B-spline in latitude, trig B-spline in longitude
bf85sph Baumgardner Frederickson 85 uniform triangulation on sphere
f90sphere Fekete 90 subdivide icosahedron
l84sph Lawson 84 l2 quadratic derivative estimate and Clough-Tocher
r84sph Renka 84 $C^1$ interpolant
ap85voronoi Augenbaum Peskin 85 iterative Voronoi
c87fejer Clutton-Brock 87 kernel smoothing
f88sph Foley 88 radial basis functions, adjusted for antipode
d86quat Duff 86 spherical B-splines
nr87sph Nielson Ramaraj 87 Interpolation over a sphere
rbg87quat Roberts Bishop Ganapathy 87 quaternions
ellipsdat near circle or ellipse
bcdp88 Boffey Cox Delves Pursglove 88 inscribed sphere
b89circle Berman 89 when fitting to circle, don't use obvious l2
cj89circle Cox Jones 89 uncertainty ellipses
rz92circle Roy Zhang 92 tight bounding circles
lp classical $L_p$ and analogous norms
converg measures of convergence
penalty penalties, smoothing, tolerances
divdiff divided differences as a measure of noise
interp interpolation
fair fair, pleasing
constr constraints
data nonstandard data
bounds bounds
multires multiple scales or resolutions
s91omega Sabin 91 fix sample h, increase frequency in trial function
l2 $l_2$
tl2 total least squares, orthogonal distance regression
li $l_\infty$, $L_\infty$
l1 $l_1$
psmooth piecewise smooth
Hausdorff Hausdorff $\max[\max_{y\in G}\min_{x\in F}\|x-y\|,\max_{y\in F}\min_{x\in G}\|x-y\|]$
statnorm statistically motivated metrics
relnorm bounding the relative error
sr80 Schonfelder Razaz
p84rel Pryce 84 generalizes Olver's rho(x,y)=abs(ln(y/x))
gauss Gauss and Legendre; see Goldstine 77 section 4.10
maxlik maximum likelihood
AIC AIC (Akaike's Information Criterion)
MRF Markov random field
dlr77 Dempster Laird Rubin 77
tt78 Tapia Thompson 78 maximum penalized likelihood
o88log O'Sullivan 88 density estimation
bgw93maxlik Bunch Gay Welsch 93 generalized NL2SOL
a73aic Akaike 73
r83band Rice 83 comparison of GCV, Cp, Akaike
a88aic Atligan 88 choice of dimension in histograms, splines, gaussians
gg84gibb Geman Geman 84 simulated annealing
mmp87 Marroquin Mitter Poggio 87 other cost funtions
weight choosing weights in $l_2$ and other norms
l2penalty $l_2 + penalty$
robustspl min $\int g''^2$ subject to $|g(t_i)-z_i| \le \epsilon$
c90diff Cullinan 90 $l_2$ subject to r-th diff not changing sign often
r80exp Ruhe 80 semi-infinite programming for sum of exponentials
b82rr Beatson 82 staying within upper and lower bounds
or86conf O'Leary Rust 86 confidence intervals for l2 with x>0
sh87pos Schmidt Hess 87 positive rational quadratic $C^1$ interpolant
sh88pos Schmidt Hess 88 positive cubic $C^1$ interpolant
oo88obst Opfer Oberle 88
dr89mono Dauner Reinsch 89 adds knots
cross-sec cross sections
spectral-data given Fourier series coefficients, as in crystallography
derivdata derivative data
intdata integral data
missing missing data
gradient given gradients, get surface; ``shape from shading''
directions given only gradient directions
potential potential, stream function
dz90dir David Zucker 90 sum elongated gaussians
w84sph Wahba 84 cross validation
ab91pot Amodei Benbourhim 91 fund. solution of iterated lapalacian, GCV
hist given integrals over small subintervals
flux given flux, get velocities
moments given moments
t88stat Thisted 88 section 4.7
spec-rat rational in cos, sin
spec-spline spectral spline
c88specrat Charron 88 like Osborne exponential fitting
g86spec Grosse 86 interpolation of Fourier series data
ds83cross Dierckx Suetens 83 tensor splines
l86set Levin 86 set-valued
gmp87sph Gmelig Meylin Pfluger 87 star-like object
s90cross Schumaker 90 interp in z, polygonalize, connect
epo91cross Ekoule Peyrin Odet 91
bs91cross Baszenski Schumaker 91 random edge swap, take good ones eventually
recontour blending methods
hb86grad Horn Brooks 86 computer vision; parallel iterative methods
l88grad Lee 88 discrete smoothing splines
cfg88grad Coughran Fichtner Grosse 88 tensor spline by conjugate gradient
bs87hist Baszenski Schumaker 87 smoothing spline, variable order
su88hist Sakai Usmani 88 shape preserving, rational
s92hist Schmidt 92 l2 smoothing with convexity by quadratic program
h87flux Handscomb 84 given integral of flux on rectangular cell edges
fgm87moment Frontini Gautschi Milovanovic 87 spline
frs88moment Frontini Rodriguez Seatzu 88 Legendre, regularization
s91moment Sablonniere 91 intermediate between Lagrange and Bernstein
v87tls Van Huffel 87 tests and speedups of total least squares
hs87prin Hastie Stuetzle 87 parametric scatterplot smooth
bdbs89odr Boggs Donaldson Byrd Schnabel 87 orthogonal distance regression
ms90odr Marin Smith 90 Hoschek algorithm
t91prin Tibshirani 91 parametric scatterplot smooth
jf87li Jing Fam 87
w88compl Watson 88 l-infinity complex function
Remez Remez exchange
li-l2 approximation by $l_2$ solution
li-over overdetermined linear system
li-under underdetermined linear system
diffcor differential correction
Hankel Hankel norm (``CF'' or ``AAK'' approximation)
t86cf Trefethen 86
st89cf Saff Totik 89 polynomial Caratheodory-Fejer fails
r86lil2 Reichel 86 polynomial approximation
bp75li Barrodale Phillips 75
b85licon Brannigan 85
sn82compl Streit Nuttall 82
s85cli Streit 85 complex
tt87li Thiran Thiry 87 canonical decomposition by Gaussian elimination for rank test
a80l1 Abdelmalek 80 overdetermined linear system
br80l1 Barrodale Roberts 80 linear equality and inequality constraints
bc80l1 Bartels Conn 80 overdetermined linear system
cj87l1 Cox Jones 87 spline l1 fitting, shape preserving
m87conv Madsen 87 min H(f(x)), f smooth, H convex
sumnorms sum of norms
o83sum Overton 83 sum 2norm(A_i x - b_i) "multifacility location"
g90sum Gurwitz 90 sum w_i abs( x - x_i )
minlen $L_2$ norm of first derivative, ``minimum length''
smoo $L_2$ norm of high derivative
smooj $l_2$ and jumps in high derivative
smoodif jumps in divided difference
smooch choice of smoothing parameter
app-curv weighted norm of second derivative to approximate curvature
plate-energy energy of thin plate
bb83minlen Baker Brolley 83 scale-free version of curve length
ikns88 Iserles Koch Norsett SanzSerna 88
hr73nat Herriot Reinsch 73 natural spline interpolation
hr76nat Herriot Reinsch 76 quintic natural spline
b78s de Boor 78 SMOOTH
imsl imsl/cssmh
d82ten Dierckx 87 netlib/dierckx/smoopy,fitpack (curfit)
w23 Whittaker 23
p70smoo Powell 70
r83band Rice 83 comparison of GCV, Cp, Akaike
r85smoo Ragozin 85 Peetre K-functional
h92reg Hansen 1992 corner in plot of norm(residual) v. seminorm(solution)
GCV generalized cross validation
s84w2nd Salkauskas 84 interpolation and piecewise constant weight
dt90curv Dudek Tsotsos 90 finite diff estimate for noisy data
qs88thin Quak Schumaker 88 calculating energy for Bernstein-Bezier patch
u81rob Utreras 81 robust splines by penalty function method
chebinterp at Chebyshev points
g78range Gaffney 78 given bound on high deriv, what possible function?
r69af Rivlin, Approximation of Functions, chap. 4
h82essen Henrici 82
s70hau Sendov 70
bwta66 Berger Webster Tapia Atkins 66 second derivative of spline * second difference of data > 0
mn87fair Meier Nowacki 87 square of second or even higher derivatives
ws88weight Wolke Schwetlick 88
t88stat Thisted 88 iteratively reweighted least squares
app-curv weighted norm of second derivative to approximate curvature
periodic periodic
monotone monotone, comonotone
convex convex
one-sided one-sided, non-negative
sconstr specialized constraints
aconstr abstract methods
oo88obst Opfer Oberle 88
branch branching
integer integer
polycon specific to polynomials
ENO ``essentially non-oscillatory'', ``total variation diminishing''
ellipticity ellipticity $\partial_{12}^2 \le \partial_{11}\partial_{22}$
cusp cusp, inflection, self-intersection
dly91reg Dyn Levin Yad-Shalom 91 integer translates of bell-shaped functions
mc91cusp Manocha Canny 91 reparameterization of formal power series
gl81wiggle Gresho Lee 81 why you should be {\em very} careful using these
heoc87eno Harten Engquist Osher Chakravarthy 87
h86eno Harten 86
zd93tvne Zhao Dai 93 C^0 O(h^3) quadratic interpolating endpoint and integral if possible
c87ellip Curtis 87
gh88int Grosse Hobby 88 spline with limited digits for coefficients and knots
sw87branch Silverman Wood 87 several curves required to coincide up to a point
semiinf semi-infinite programming
mu88hilbert Micchelli Utreras 88 orthogonal projection of adjoint interp, dual
r80exp Ruhe 80 semi-infinite programming for sum of exponentials
gr81semi Glashoff Roleff 81 complex
b87semi Bosworth 87 semi-infinite programming
t88remez Tang 88 single-exchange Remez
fm92semi Fischer Modersitzki 92 primal dual method
l83per Lucas 83 add polynomial correction terms to increase convergence order
m86persmoo McDonald 86 scatterplot smooth of $f(\omega t)$
r86perspl Radziewski 86 periodic spline on uniform grid
d87fit Dierckx 87 percur
sb88derper Shelley Baker 88 full-order accurate derivatives
s91bern Stockler 91 multivariate Bernoulli spline
monquad quadratic
moncub cubic
monrat rational quadratic
mono-biv bivariate
mono-other monotone, other forms or general order
cf91mono Carlson Fritsch 91 issues in comonotonicity
r80con Roulier 80 survey
s83mon Schumaker 83
bz85mon Beatson Ziegler 85 bivariate interpolation
gu88shape Goodman Unsworth 88 G^1 Bezier
fc80mono Fritsch Carlson 80
cu80mono Correa Utreras 80 min $\int s''^2$
h83mono Hyman 83
ds85dual Dietze Schmidt 85 dual nonlinear program
v86mono Varas 86 Laurent spline sequence, Gauss Seidel
dd87mono Davis Dowden 87 ``ratio slope method''
dr89mono Dauner Reinsch 89 adds knots
ms97mono Manni Sablonniere 97 local, $C^2 O(h^3)$
moncub4 $O(h^4)$
ejl85mono Eisenstat Jackson Lewis 85 $O(h^4)$ variant of Fritsch Carlson
y87mono Yan 87
bw88mono Beatson Wolkowicz 88 more fit-and-modify algorithms
gm91mono Gasparo Morandi 91 match f, f' and break interval if necessary
dg85rat Delbourgo Gregory 85 C1 rational quadratic interpolation
sh87pos Schmidt Hess 87 positive rational quadratic $C^1$ interpolant
bz85mon Beatson Ziegler 85 bivariate interpolation
cgr86vd Coughran Grosse Rose 86 tensor product of variation diminishing
cf87bimond Fritsch Carlson 85 bivariate interpolation
cf89unimond Fritsch Carlson 89 bivariate interpolation, monotone in one variable
cf90mono Costantini Fontanella 91 hermite data; raise degree until mono
uv91scat Utreras Varas 91 monotone thin plate spline for scattered data
ddm92mono Dahmen DeVore Micchelli 92 subst x=(f(x,1)-f(x,0)-c)/c in bilinear
sh93ratspl Schmidt Hess 93 C^2 rational bicubic
bs77mono de Boor Swartz 77 interpolating spline of arbitrary order, deficiency 1
cgr86vd Coughran Grosse Rose 86 tensor product of variation diminishing
ss86rat Sakai Silanes 86
r87tension Renka 87 choice of tension parameters for shape preservation
cj87l1 Cox Jones 87 B-spline coefficient difference as sufficient condition
r88monospl Ramsey 88 integrals of B-splines, nonnegative coefficients
convquad quadratic
convcub cubic
convsmoo with penalty term for smoothing
conv-other convex, other forms
mr78convex McAllister Roulier 78 convex quadratic by knot insertion
r80con Roulier 80 survey
b82convex Beatson 82 convex quadratic spline
gu88shape Goodman Unsworth 88 G^1 Bezier
b78s de Boor 78 TAUTSP
s87dual Schmidt 87 dual for convex C1 cubic
s91dual Schmidt 91 stay within intervals, min mean curvature
ims86convex Irvine Marin Smith 86 convex spline interpolation and smoothing
ae87convex Andersson Elving 87 interpolation
ea88convex Andersson Elving 87 smoothing by Newton method
n80convex Neuman 80 interpolating spline of arbitrary order, deficiency 1
d80convex Dierckx 80 quadratic programming
cd84conv Chang Davis 84 convexity of Bernstein polynomials on triangles
s84tri Scott 84 checking scattered 2d data for convexity
c87moncon Costantini 86 monotone and/or convex, general degree
r87tension Renka 87 choice of tension parameters for shape preservation
cj87l1 Cox Jones 87 B-spline coefficient difference as sufficient condition
ffj88shape Ferguson Frank Jones 88 convex slices
d91conv Dahmen 91 survey
sh93ratspl Schmidt Hess 93 C^2 rational bicubic
noise recognizing noise
outlier recognizing outliers and influential points
redundancy recognizing redundancy
B-diag diagnostics specific to B-splines
gdiag diagnostic graphics
testing tests, benchmarks
gt74noise Guerra Tapia 74 residual from 6-point spline interpolant
o80der Oliver 80 differentiation of fairly accurate function values
s77stat Seber 77 statistics
m84diag Maindonald 84
g90diag Gu 90 treat as retrospective linear model; compute column cosines
m73Cp Mallows 73 $C_p$ plots to choose subsets in regression
t77eda Tukey Exploratory Data Analysis
ah84micro Alfeld Harris 84 MICROSCOPE plotting to check smoothness
bc87brush Becker Cleveland 87 simultaneous identification in scatterplot matrix
ht88infl Hastie Tibshirani 88 equivalent kernel; eigenfunc of smoother
contouring contouring