Subject: NA Digest, V. 93, # 27
Subject: NA Digest, V. 93, # 27
NA Digest Sunday, July 25, 1993 Volume 93 : Issue 27
Today's Editor:
Cleve Moler
The MathWorks, Inc.
moler@mathworks.com
Today's Topics:
Moving Boundary Problems
Elliptic PDE Solver Sought
Numerical Mathematics, A Laboratory Approach
Eigensystem Solver for Pentadiagonal Systems
Workshop at Bath
Post Doc Position at Battelle Pacific Northwest Laboratory
Contents: Linear Algebra and its Applications
Submissions for NA Digest:
Mail to na.digest@na-net.ornl.gov.
Information about NA-NET:
Mail to na.help@na-net.ornl.gov.
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From: Pasqua D'Ambra
Date: Thu, 22 Jul 93 13:26:13 EDT
Subject: Moving Boundary Problems
I am a Ph.D. Student and I am working on my thesis.
The subject is "Moving boundary problems (Stefan Problems)".
I would like to have contacts with other researchers in the field and
I would like to receive recent references about resolution of these problems
on parallel machines.
PASQUA D'AMBRA PHONE: +39 81 675624
Universita' di Napoli FAX : +39 81 7662106
dip. matematica e applicazioni E-MAIL: PASQUA@VM.CISED.UNINA.IT
80126 Napoli Italia
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From: Vladimir Oliker
Date: Mon, 19 Jul 93 09:32:37 -0400
Subject: Elliptic PDE Solver Sought
I am looking for a high accuracy linear elliptic PDE-solver that can
deal with general boundary conditions in 2-d domains with curved boundaries;
for example, on an ellipse.
Any help will be greatly appreciated.
Vladimir Oliker
oliker@mathcs.emory.edu
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From: Eugene Isaacson
Date: Tue, 20 Jul 1993 16:18:42 -0500 (EST)
Subject: Numerical Mathematics, A Laboratory Approach
Just Published.
"Numerical Mathematics - A Laboratory Approach", by Shlomo Breuer & Gideon Zwas
Cambridge University Press, 267 p.
Most noteworthy for its unique use of the microcomputer laboratory to
treat algorithmic aspects of mathematics - without calculus or linear algebra.
Here is a mathematically rigorous development in eight chapters:
1. Mathematics in a numerical laboratory;
2. Iterations for root extractions;
3. Area approximations;
4. Linear systems - an algorithmic approach;
5. Algorithmic computations of pi and e;
6. Convergence acceleration;
7. Interpolative approximation;
8. Computer library functions.
Suitable for first year college students; training mathematics teachers;
and gifted high school students.
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From: Imran Bhutta
Date: Wed, 21 Jul 93 11:20:56 EDT
Subject: Eigensystem Solver for Pentadiagonal Systems
Dear Editor(s),
I am developing a Semiconductor Device Simulator using Quantum
Mechanical approach. It is a 2-D simulator and at one point involves the
solution of the Schrodinger's equation. That is to say I have to find the
eigenvalues and corresponding eigenvectors for that system of equations. For
a 2-D system with 100 points in 'x' and 'y' directions, my eigen system matrix
is a n**2 by n**2 i.e., 10,000 by 10,000. This matrix is a pentadiagonal
matrix, with a diagonal vector and two subdiagonals and two superdiagonals.
The subdiagonals lie at 'i-1' and 'i-5' and the superdiagonals lie at 'i+1' and
'i+5'. It is a highly sparse matrix, which is real and symmetric.
I am looking for a routine that would help me solve this
pentadiagonal eigen system. I have routines for tridiagonal systems, and my
first approach was to reduce my pentadiagonal matrix to a tridiagonal form by
Householder's scheme. However Householder's scheme generates an orthogonal
matrix alongwith the tridiagonal matrix, and I do not gain any advantage in
space saving, since the orthogonal matrix is not pentadiagonal. If someone
can suggest a solution technique I would appreciate it very much. My e-mail
address is BHUTTA@VTVM1.CC.VT.EDU. I appreciate your help very much. Thank
you.
Imran A. Bhutta
EE Department
Virginia Tech
Blacksburg, VA 24061-0111
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From: I. G. Graham
Date: Mon, 19 Jul 93 9:57:34 BST
Subject: Workshop at Bath
Dear Colleagues,
This is to inform you that there will be an informal workshop on iterative
methods for PDE at the University of Bath, U.K. on September 6th 1993.
The two principal speakers are Professor Wolfgang Hackbusch (University of
Kiel, Germany) and Professor Dan Sorensen (Rice University, Texas).
There will also be a number of contributed talks from U.K. researchers.
Best wishes,
Ivan Graham (igg@maths.bath.ac.uk)
Iterative methods for large computational problems arising from PDEs
A Workshop at the University of Bath
Monday 6th September 1993 -- Building 6E, Room 2.2
Wolfgang Hackbusch (Christian Albrechts Universit\"{a}t, Kiel, Germany):
On the frequency decomposition multi-grid method.
Kevin Parrott and Tony Ware (Oxford University Computing Laboratory):
Parallel multi-grid for a 3-D tensor diffusion problem with block-discontinuous
coefficients
Mike Wilson (School of Mechanical Engineering, University of Bath):
Parallel multi-grid computation of rotating disc flows
Paul Crumpton (Oxford University Computing Laboratory):
Multi-grid for non-nested grids on a parallel computer
Dan Sorensen (Rice University):
Variations on Arnoldi's method for large scale eigenvalue problems
Mark Hagger and Alastair Spence (School of Mathematical Sciences, Bath):
Polynomial preconditioning for conjugate gradient methods
Rob Coomer and Ivan Graham (School of Mathematical Sciences, Bath):
Mesh-independent fixed point iteration and domain decomposition
for semiconductor device equations in 2D
All interested persons are welcome to attend. There will be no
registration fee. However, in order that we can inform the catering
department about the numbers for lunch it would be helpful if those
who intend to come could inform us before August 27th by email
to Ivan Graham at igg@maths.bath.ac.uk or by telephone to Sarah Love
at (0225) 826198 or School of Mathematical Sciences, University of Bath,
Bath BA2 7AY, U.K.
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From: George Fann
Date: Wed, 21 Jul 93 10:03:56 PDT
Subject: Post Doc Position at Battelle Pacific Northwest Laboratory
Post-doc Opening starting Oct. 1993
Battelle Pacific Northwest Laboratory
The Analytic Sciences Department of the Pacific Northwest Laboratory
is inviting applications for a postdoctoral research position. The
appointment is initially for a one-year term. The successful
candidate will participate in a project for computational fluid
dynamics and numerical linear algebra algorithms for MIMD parallel
computers ( e.g. Touchstone DELTA, or clusters of HP 9000/735 and IBM
RS6000/560 workstations).
We are looking for an individual to implement and investigate recent
algorithm advances in solving elliptic and parabolic equations using
the finite volume formulation.
This project is interdisciplinary in nature and interfaces with
efforts in numerical analysis, parallel computing, large-scale
simulation of physical processes, and programming tools. Project
members have access to state-of-the art computing facilities,
including a 520-processor Intel Touchstone DELTA. Nominal
requirements include a Ph.D. in computer science, applied mathematics,
or an applied science or engineering discipline. A good algorithms
background and hands-on experience in some aspect of scientific
computing is necessary.
Applications must be addressed to George Fann, ms: K7-15 Pacific
Northwest Laboratory, Battelle Blvd, Richland, WA 99352, or via e-mail
to gi_fann@pnl.gov. The application must include a resume and the
names and addresses of three references.
For further information, contact George Fann, gi_fann@pnl.gov.
Fax:(509) 375-3641.
Battelle is an affirmative action/equal opportunity employer. Legal
right to work in U.S. is required -- U.S. Citizenship preferred.
Pacific Northwest Laboratory is a U.S. Department of Energy
laboratory.
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From: Richard Brualdi
Date: Wed, 21 Jul 1993 08:36:20 -0500 (CDT)
Subject: Contents: Linear Algebra and its Applications
LINEAR ALGEBRA AND ITS APPLICATIONS
Contents Volumes 188/189
Preface 1
Dario Bini (Pisa, Italy) and Victor Pan (Bronx, New York)
Improved Parallel Computations With Toeplitz-like
and Hankel-like Matrices 3
Adam W. Bojanczyk (Ithaca, New York), James G. Nagy (Dallas, Texas),
and Robert J. Plemmons (Winston-Salem, North Carolina)
Block RLS Using Row Householder Reflections 31
Stephen Boyd (Stanford, California) and Laurent El Ghaoui
(Paris, France)
Method of Centers for Minimizing Generalized Eigenvalues 63
Ralph Byers (Lawrence, Kansas) and N. K. Nichols
(Reading, United Kingdom)
On the Stability Radius of a Generalized State-Space System 113
Biswa Nath Datta and Fernando Rincon (De Kalb, Illinois)
Feedback Stabilization of a Second-Order System:
A Nonmodal Approach 135
Bart De Moor (Leuven, Belgium)
Structured Total Least Squares and L2 Approximation Problems 163
Ludwig Elsner and Chunyang He (Bielefeld, Deutschland)
Perturbation and Interlace Theorems for the Unitary
Eigenvalue Problem 207
Michael K. H. Fan (Atlanta, Georgia)
A Quadratically Convergent Local Algorithm on Minimizing
the Largest Eigenvalue of a Symmetric Matrix 231
Roland W. Freund (Murray Hill, New Jersey) and Hongyuan Zha
(University Park, Pennsylvania)
Formally Biorthogonal Polynomials and a Look-ahead
Levinson Algorithm for General Toeplitz Systems 255
Mei Gao and Michael Neumann (Storrs, Connecticut)
A Global Minimum Search Algorithm for Estimating the
Distance to Uncontrollability 305
Martin H. Gutknecht (Zurich, Switzerland)
Stable Row Recurrences for the Pade Table and
Generically Superfast Lookahead Solvers for
Non-Hermitian Toeplitz Systems 351
A. Scottedward Hodel (Auburn, Alabama)
Computation of System Zeros With Balancing 423
W. W. Lin (Hsin-Chu, Taiwan) and S. S. You (Chung-Li, Taiwan)
A Symplectic Acceleration Method for the Solution
of the Algebraic Riccati Equation on a Parallel
Computer 437
Lin-Zhang Lu (Fujian, China) and Wen-Wei Lin (Hsinchu, Taiwan)
An Iterative Algorithm of the Solution of the
Discrete-Time Algebraic Riccati Equation 465
Alexander N. Malyshev (Novosibirsk, Russia)
Parallel Algorithm for Solving Some Spectral Problems
of Linear Algebra 489
Pradeep Misra (Dayton, Ohio) and Thulasinath Manickam
(Kingston, Rhode Island)
Balanced Realization of Separable-Denominator
Multidimensional Systems 521
Marc Moonen (Heverlee, Belgium), Paul Van Dooren
(Urbana, Illinois), and Filiep Vanpoucke (Heverlee, Belgium)
On the QR Algorithm and Updating the SVD and
the URV Decomposition in Parallel 549
W. H. L. Neven (Emmeloord, the Netherlands) and C. Praagman
(Groningen, the Netherlands)
Column Reduction of Polynomial Matrices 569
R. V. Patel (Montreal, Quebec, Canada)
On Computing the Eigenvalues of a Symplectic Pencil 591
Vassilis Syrmos (Honolulu, Hawaii) and Petr Zagalak
(Prague, Czechoslovakia)
Computing Normal External Descriptions and Feedback Design 613
David H. Wood (Newark, Delaware)
Product Rules for the Displacement of Near-Toeplitz Matrices 641
Dragan Zigic, Layne T. Watson, and Christopher Beattie
(Blacksburg, Virginia)
Contragredient Transformations Applied to the Optimal
Projection Equations 665
Author Index 677
LINEAR ALGEBRA AND ITS APPLICATIONS
Contents Volume 190
Jack B. Brown (Auburn, Alabama), Phillip J. Chase
(Ft. Meade, Maryland), and Arthur O. Pittenger
(Baltimore, Maryland)
Order Independence and Factor Convergence in Iterative
Scaling 1
James S. Otto (Denver, Colorado)
Multigrid Convergence for Convection-Diffusion Problems
on Composite Grids 39
Hassane Sadok (Villeneuve d'Ascq-Cedex, France)
Quasilinear Vector Extrapolation Methods 71
Han H. Cho (Seoul, Korea)
Prime Boolean Matrices and Factorizations 87
J. B. Wilker (Scarborough, Ontario, Canada)
The Quaternion Formalism for Mobius Groups in Four
or Fewer Dimensions 99
Martin Hanke (Karlsruhe, Germany) and Michael Neumann
(Storrs, Connecticut)
The Geometry of the Set of Scaled Projections 137
Joel E. Cohen (New York, New York) and Uriel G. Rothblum
(Haifa, Israel)
Nonnegative Ranks, Decompositions, and Factorizations
of Nonnegative Matices 149
Carolyn A. Eschenbach (Atlanta, Georgia) and Charles R. Johnson
(Williamsburg, Virginia)
Sign Patterns That Require Repeated Eigenvalues 169
Raymond H. Chan and Kwok-Po Ng (Hong Kong, People's
Republic of China)
Toeplitz Preconditioners for Hermitian Toeplitz Systems 181
Roger A. Horn (Salt Lake City, Utah) and Dennis I. Merino
(Hammond, Louisiana)
A Real-Coninvolutory Analog of the Polar Decomposition 209
M. H. Lim (Kuala Lumpur, Malaysia)
A Note on Similarity Preserving Linear Maps on Matrices 229
Miroslav Fiedler and Zdenek Vavrin
(Praha, Czech Republic)
Polynomials Compatible With a Symmetric Loewner Matrix 235
William A. Adkins (Baton Rouge, Louisiana), Jean-Claude Evard
(Laramie, Wyoming), and Robert M. Guralnick
(Los Angeles, California)
Matrices Over Differential Fields Which Commute With Their
Derivative 253
Author Index 263
Contents 190, September
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End of NA Digest
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