Index

ad hoc SOR method

seemethod, ad hoc SOR

asynchronous method

seemethod, asynchronous

Bi-CGSTAB method

seemethod, Bi-CGSTAB

Bi-Conjugate Gradient Stabilized method

seemethod, Bi-CGSTAB

bi-orthogonality

in BiCG

BiConjugate Gradient (BiCG)

in QMR

Quasi-Minimal Residual (QMR)

BiCG method

seemethod, BiCG

BiConjugate Gradient method

seemethod, BiCG

BLAS

Why Use Templates?

BLAS

CRS-based Factorization Solve

block methods

(, )

breakdown

avoiding by look-ahead

Convergence

in Bi-CGSTAB

Convergence

in BiCG

Convergence, Convergence, Convergence, Quasi-Minimal Residual (QMR)

in BiCG

Convergence, Convergence, Convergence, Quasi-Minimal Residual (QMR)

in BiCG

Convergence, Convergence, Convergence, Quasi-Minimal Residual (QMR)

in BiCG

Convergence, Convergence, Convergence, Quasi-Minimal Residual (QMR)

in CG for indefinite systems

MINRES and SYMMLQ

CG method

seemethod, CG

CGNE method

seemethod, CGNE

CGNR method

seemethod, CGNR

CGS method

seemethod, CGS

chaotic method

seemethod, asynchronous

Chebyshev iteration

seemethod, Chebyshev iteration

codes

C++

Why Use Templates?

FORTRAN

Why Use Templates?

MATLAB

Why Use Templates?

complex systems

(, )

Conjugate Gradient method

seemethod, CG

Conjugate Gradient Squared method

seemethod, CGS

convergence

irregular

Glossary

irregular

Glossary

irregular

Glossary

irregular

Glossary

irregular

Glossary

irregular

Glossary

linear

Glossary

of Bi-CGSTAB

(, )

of Bi-CGSTAB

(, )

of BiCG

(, )

of BiCG

(, )

of CG

(, )

of CG

(, )

of CGNR and CGNE

Theory

of CGS

(, )

of CGS

(, )

of Chebyshev iteration

(, )

of Chebyshev iteration

(, )

of Gauss-Seidel

The Gauss-Seidel Method

of Jacobi

(, )

of Jacobi

(, )

of MINRES

MINRES and SYMMLQ

of QMR

(, )

of QMR

(, )

of SSOR

The Symmetric Successive

smooth

Glossary

smooth

Glossary

stalled

Glossary

stalled

Glossary

stalled

Glossary

superlinear

Glossary

superlinear

Glossary

superlinear

Glossary

superlinear

Glossary

data structures

(, )

diffusion

artificial

Modified incomplete factorizations

domain decomposition

multiplicative Schwarz

(, )

multiplicative Schwarz

(, )

non-overlapping subdomains

(, )

non-overlapping subdomains

(, )

overlapping subdomains

(, )

overlapping subdomains

(, )

Schur complement

Domain Decomposition Methods

Schwarz

Domain Decomposition Methods

fill-in strategies

seepreconditioners, point incomplete"factorizations

FORTRAN codes

seecodes, FORTRAN

Gauss-Seidel method

seemethod, Gauss-Seidel

Generalized Minimal Residual method

seemethod, GMRES

GMRES method

seemethod, GMRES

ill-conditioned systems

using GMRES on

Implementation

implementation

of Bi-CGSTAB

(, )

of Bi-CGSTAB

(, )

of BiCG

(, )

of BiCG

(, )

of CG

(, )

of CG

(, )

of CGS

(, )

of CGS

(, )

of Chebyshev iteration

(, )

of Chebyshev iteration

(, )

of GMRES

(, )

of GMRES

(, )

of QMR

(, )

of QMR

(, )

IMSL

Introduction

inner products

as bottlenecks

Implementation, Chebyshev Iteration, Comparison with other

as bottlenecks

Implementation, Chebyshev Iteration, Comparison with other

as bottlenecks

Implementation, Chebyshev Iteration, Comparison with other

avoiding with Chebyshev

Chebyshev Iteration, Comparison with other , Comparison with other , Implementation

avoiding with Chebyshev

Chebyshev Iteration, Comparison with other , Comparison with other , Implementation

avoiding with Chebyshev

Chebyshev Iteration, Comparison with other , Comparison with other , Implementation

avoiding with Chebyshev

Chebyshev Iteration, Comparison with other , Comparison with other , Implementation

irregular convergence

seeconvergence, irregular

ITPACK

Choosing the Value

Jacobi method

seemethod, Jacobi

Krylov subspace

Theory

Lanczos

and CG

Theory, (, )

and CG

Theory, (, )

and CG

Theory, (, )

LAPACK

Introduction

linear convergence

seeconvergence, linear

LINPACK

Introduction

MATLAB codes

seecodes, MATLAB

method

ad hoc SOR

Notes and References

adaptive Chebyshev

Chebyshev Iteration, Comparison with other

adaptive Chebyshev

Chebyshev Iteration, Comparison with other

asynchronous

Notes and References

Bi-CGSTAB

What Methods Are , Overview of the , (ii, )

Bi-CGSTAB

What Methods Are , Overview of the , (ii, )

Bi-CGSTAB

What Methods Are , Overview of the , (ii, )

Bi-CGSTAB

What Methods Are , Overview of the , (ii, )

Bi-CGSTAB2

Convergence

BiCG

What Methods Are , Overview of the , (ii, )

BiCG

What Methods Are , Overview of the , (ii, )

BiCG

What Methods Are , Overview of the , (ii, )

BiCG

What Methods Are , Overview of the , (ii, )

CG

What Methods Are , Overview of the , (ii, )

CG

What Methods Are , Overview of the , (ii, )

CG

What Methods Are , Overview of the , (ii, )

CG

What Methods Are , Overview of the , (ii, )

CG

What Methods Are , Overview of the , (ii, )

CGNE

What Methods Are , Overview of the , (ii, )

CGNE

What Methods Are , Overview of the , (ii, )

CGNE

What Methods Are , Overview of the , (ii, )

CGNE

What Methods Are , Overview of the , (ii, )

CGNR

What Methods Are , Overview of the , (ii, )

CGNR

What Methods Are , Overview of the , (ii, )

CGNR

What Methods Are , Overview of the , (ii, )

CGNR

What Methods Are , Overview of the , (ii, )

CGS

What Methods Are , Overview of the , (ii, )

CGS

What Methods Are , Overview of the , (ii, )

CGS

What Methods Are , Overview of the , (ii, )

CGS

What Methods Are , Overview of the , (ii, )

chaotic

Notes and References, seemethod, asynchronous

chaotic

Notes and References, seemethod, asynchronous

Chebyshev iteration

What Methods Are , Iterative Methods, Overview of the , (ii, )

Chebyshev iteration

What Methods Are , Iterative Methods, Overview of the , (ii, )

Chebyshev iteration

What Methods Are , Iterative Methods, Overview of the , (ii, )

Chebyshev iteration

What Methods Are , Iterative Methods, Overview of the , (ii, )

Chebyshev iteration

What Methods Are , Iterative Methods, Overview of the , (ii, )

Chebyshev iteration

What Methods Are , Iterative Methods, Overview of the , (ii, )

Chebyshev iteration

What Methods Are , Iterative Methods, Overview of the , (ii, )

Chebyshev iteration

What Methods Are , Iterative Methods, Overview of the , (ii, )

domain decomposition

(ii, )

domain decomposition

(ii, )

Gauss-Seidel

What Methods Are , Overview of the , Stationary Iterative Methods, (ii, )

Gauss-Seidel

What Methods Are , Overview of the , Stationary Iterative Methods, (ii, )

Gauss-Seidel

What Methods Are , Overview of the , Stationary Iterative Methods, (ii, )

Gauss-Seidel

What Methods Are , Overview of the , Stationary Iterative Methods, (ii, )

Gauss-Seidel

What Methods Are , Overview of the , Stationary Iterative Methods, (ii, )

GMRES

What Methods Are , Overview of the , (ii, )

GMRES

What Methods Are , Overview of the , (ii, )

GMRES

What Methods Are , Overview of the , (ii, )

GMRES

What Methods Are , Overview of the , (ii, )

Jacobi

What Methods Are , Overview of the , Stationary Iterative Methods, (ii, )

Jacobi

What Methods Are , Overview of the , Stationary Iterative Methods, (ii, )

Jacobi

What Methods Are , Overview of the , Stationary Iterative Methods, (ii, )

Jacobi

What Methods Are , Overview of the , Stationary Iterative Methods, (ii, )

Jacobi

What Methods Are , Overview of the , Stationary Iterative Methods, (ii, )

MINRES

What Methods Are , Overview of the , (ii, )

MINRES

What Methods Are , Overview of the , (ii, )

MINRES

What Methods Are , Overview of the , (ii, )

MINRES

What Methods Are , Overview of the , (ii, )

of simultaneous displacements

seemethod, Jacobi

of successive displacements

seemethod, Gauss-Seidel

QMR

What Methods Are , Overview of the , (ii, )

QMR

What Methods Are , Overview of the , (ii, )

QMR

What Methods Are , Overview of the , (ii, )

QMR

What Methods Are , Overview of the , (ii, )

relaxation

Notes and References, Notes and References

relaxation

Notes and References, Notes and References

SOR

What Methods Are , Overview of the , Stationary Iterative Methods, (ii, )

SOR

What Methods Are , Overview of the , Stationary Iterative Methods, (ii, )

SOR

What Methods Are , Overview of the , Stationary Iterative Methods, (ii, )

SOR

What Methods Are , Overview of the , Stationary Iterative Methods, (ii, )

SOR

What Methods Are , Overview of the , Stationary Iterative Methods, (ii, )

SOR

What Methods Are , Overview of the , Stationary Iterative Methods, (ii, )

SOR

What Methods Are , Overview of the , Stationary Iterative Methods, (ii, )

SSOR

What Methods Are , Overview of the , Stationary Iterative Methods, (ii, )

SSOR

What Methods Are , Overview of the , Stationary Iterative Methods, (ii, )

SSOR

What Methods Are , Overview of the , Stationary Iterative Methods, (ii, )

SSOR

What Methods Are , Overview of the , Stationary Iterative Methods, (ii, )

SSOR

What Methods Are , Overview of the , Stationary Iterative Methods, (ii, )

SYMMLQ

What Methods Are , Overview of the , (ii, )

SYMMLQ

What Methods Are , Overview of the , (ii, )

SYMMLQ

What Methods Are , Overview of the , (ii, )

SYMMLQ

What Methods Are , Overview of the , (ii, )

minimization property

in Bi-CGSTAB

Convergence

in CG

Theory, MINRES and SYMMLQ

in CG

Theory, MINRES and SYMMLQ

in MINRES

MINRES and SYMMLQ

MINRES method

seemethod, MINRES

multigrid

(, )

NAG

Introduction

nonstationary methods

(, )

normal equations

Overview of the , Overview of the

overrelaxation

Choosing the Value

parallelism

(, )

in BiCG

Implementation

in CG

Implementation

in Chebyshev iteration

Implementation

in GMRES

Implementation, Implementation

in GMRES

Implementation, Implementation

in QMR

Implementation

inner products

(, )

inner products

(, )

matrix-vector products

(, )

matrix-vector products

(, )

vector updates

Vector updates

preconditioners

(, )

ADI

(, )

ADI

(, )

ADI

(, )

block factorizations

(, )

block factorizations

(, )

block tridiagonal

(, )

block tridiagonal

(, )

central differences

(, )

central differences

(, )

cost

(, )

cost

(, )

fast solvers

(, )

fast solvers

(, )

incomplete factorization

(, )

incomplete factorization

(, )

left

Left and right

point incomplete factorizations

(, )

point incomplete factorizations

(, )

point incomplete factorizations

(, )

point incomplete factorizations

(, )

point incomplete factorizations

(, )

point incomplete factorizations

(, )

point incomplete factorizations

(, )

point incomplete factorizations

(, )

point incomplete factorizations

(, )

point incomplete factorizations

(, )

point incomplete factorizations

(, )

point incomplete factorizations

(, )

point Jacobi

(, )

point Jacobi

(, )

polynomial

(, )

polynomial

(, )

reduced system

(, )

reduced system

(, )

right

Left and right

SSOR

(, )

SSOR

(, )

SSOR

(, )

symmetric part

(, )

symmetric part

(, )

QMR method

seemethod, QMR

Quasi-Minimal Residual method

seemethod, QMR

relaxation method

seemethod, relaxation

residuals

in BiCG

BiConjugate Gradient (BiCG)

in CG

Conjugate Gradient Method

in CG

Conjugate Gradient Method

restarting

in BiCG

Convergence

in GMRES

Generalized Minimal Residual , Theory, Implementation

in GMRES

Generalized Minimal Residual , Theory, Implementation

in GMRES

Generalized Minimal Residual , Theory, Implementation

row projection methods

(, )

search directions

in BiCG

BiConjugate Gradient (BiCG)

in CG

Conjugate Gradient Method , Conjugate Gradient Method , Theory

in CG

Conjugate Gradient Method , Conjugate Gradient Method , Theory

in CG

Conjugate Gradient Method , Conjugate Gradient Method , Theory

in CG

Conjugate Gradient Method , Conjugate Gradient Method , Theory

smooth convergence

seeconvergence, smooth

software

obtaining

(ii, )

obtaining

(ii, )

SOR method

seemethod, SOR

sparse matrix storage

(, )

BCRS

(, )

BCRS

(, )

CCS

(, )

CCS

(, )

CDS

(, )

CDS

(, )

CRS

(, )

CRS

(, )

JDS

(, )

JDS

(, )

SKS

(, )

SKS

(, )

SSOR method

seemethod, SSOR

stalled convergence

seeconvergence, stalled

Stationary methods

(, )

stopping criteria

(, )

Successive Overrelaxation method

seemethod, SOR

superlinear convergence

seeconvergence, superlinear

Symmetric LQ method

seemethod, SYMMLQ

Symmetric Successive Overrelaxation method

seemethod, SSOR

SYMMLQ method

seemethod, SYMMLQ

template

Introduction

three-term recurrence

in CG

Theory

two-term recurrence

Implementation

underrelaxation

Choosing the Value

wavefronts

seepreconditioners, point incomplete factorizations, wavefronts in