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Index

ad hoc SOR method

see method, ad hoc SOR

asynchronous method

see method, asynchronous

Bi-CGSTAB method

see method, Bi-CGSTAB

Bi-Conjugate Gradient Stabilized method

see method, Bi-CGSTAB

bi-orthogonality

in BiCG

BiConjugate Gradient (BiCG)

in QMR

Quasi-Minimal Residual (QMR)

BiCG method

see method, BiCG

BiConjugate Gradient method

see method, BiCG

BLAS

Why Use Templates?, 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 CG for indefinite systems

MINRES and SYMMLQ

CG method

see method, CG

CGNE method

see method, CGNE

CGNR method

see method, CGNR

CGS method

see method, CGS

chaotic method

see method, asynchronous

Chebyshev iteration

see method, Chebyshev iteration

codes

FORTRAN

Why Use Templates?

MATLAB

Why Use Templates?

complex systems

(, )

Conjugate Gradient method

see method, CG

Conjugate Gradient Squared method

see method, CGS

convergence

irregular

Iterative Methods, Glossary

irregular

Iterative Methods, Glossary

irregular

Iterative Methods, Glossary

linear

Iterative Methods, Glossary

of Bi-CGSTAB

(, )

of BiCG

(, )

of CG

(, )

of CGNR and CGNE

Theory

of CGS

(, )

of Chebyshev iteration

(, )

of Gauss-Seidel

The Gauss-Seidel Method

of Jacobi

(, )

of MINRES

MINRES and SYMMLQ

of QMR

(, )

of SSOR

The Symmetric Successive

smooth

Iterative Methods, Glossary

stalled

Iterative Methods, Glossary

superlinear

Iterative Methods, Glossary

superlinear

Iterative Methods, Glossary

data structures

(, )

domain decomposition

multiplicative Schwarz

(, )

non-overlapping subdomains

(, )

overlapping subdomains

(, )

Schur complement

Domain Decomposition Methods

Schwarz

Domain Decomposition Methods

FORTRAN codes

see code, FORTRAN

Gauss-Seidel method

see method, Gauss-Seidel

Generalized Minimal Residual method

see method, GMRES

GMRES method

see method, GMRES

ill-conditioned systems

using GMRES on

Implementation

implementation

of Bi-CGSTAB

(, )

of BiCG

(, )

of CG

(, )

of CGS

(, )

of Chebyshev iteration

(, )

of GMRES

(, )

of QMR

(, )

IMSL

Introduction

inner products

as bottlenecks

Implementation, Chebyshev Iteration, Comparison with other

avoiding with Chebyshev

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

irregular convergence

see convergence, irregular

ITPACK

Choosing the Value

Jacobi method

see method, Jacobi

Krylov subspace

Theory

Lanczos

and CG

Theory, (, )

LAPACK

Introduction

linear convergence

see convergence, linear

LINPACK

Introduction

MATLAB codes

see code, MATLAB

method

ad hoc SOR

Notes and References

adaptive Chebyshev

Chebyshev Iteration, Comparison with other

asynchronous

Notes and References

Bi-CGSTAB

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

Bi-CGSTAB2

Convergence

BiCG

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

CG

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

CGNE

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

CGNR

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

CGS

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

chaotic

Notes and References, see method, asynchronous

Chebyshev iteration

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

domain decomposition

(ii, )

Gauss-Seidel

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

GMRES

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

Jacobi

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

MINRES

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

of simultaneous displacements

see method, Jacobi

of successive displacements

see method, Gauss-Seidel

QMR

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

relaxation

Notes and References, Notes and References

SOR

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, )

minimization property

in Bi-CGSTAB

Convergence

in CG

Theory, MINRES and SYMMLQ

in MINRES

MINRES and SYMMLQ

MINRES method

see method, 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 QMR

Implementation

inner products

(, )

matrix-vector products

(, )

vector updates

Vector updates

preconditioners

(, )

ADI

(, )

block factorizations

(, )

block tridiagonal

(, )

central differences

(, )

cost

(, )

fast solvers

(, )

incomplete factorization

(, )

left

Theoretical prerequisites on

point incomplete factorizations

(, )

point Jacobi

(, )

polynomial

(, )

reduced system

(, )

right

Theoretical prerequisites on

SSOR

(, )

symmetric part

(, )

QMR method

see method, QMR

Quasi-Minimal Residual method

see method, QMR

relaxation method

see method, relaxation

residuals

in BiCG

BiConjugate Gradient (BiCG)

in CG

Conjugate Gradient Method

restarting

in BiCG

Convergence

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

smooth convergence

see convergence, smooth

software

obtaining

(ii, )

SOR method

see method, SOR

sparse matrix storage

(, )

BCRS

(, )

CCS

(, )

CDS

(, )

CRS

(, )

JDS

(, )

SKS

(, )

SSOR method

see method, SSOR

stalled convergence

see convergence, stalled

Stationary methods

(, )

stopping criteria

(, )

Successive Overrelaxation method

see method, SOR

superlinear convergence

see convergence, superlinear

Symmetric LQ method

see method, SYMMLQ

Symmetric Successive Overrelaxation method

see method, SSOR

SYMMLQ method

see method, SYMMLQ

template

Introduction

three-term recurrence

in CG

Theory

two-term recurrence

Implementation

underrelaxation

Choosing the Value