稀疏线性系统的迭代方法：第2版

PrefacetotheSecondEdition

PrefacetotheFirstEdition

1BackgroundinLinearAlgebra

1.1Matrices

1.2SquareMatricesandEigenvalues

1.3TypesofMatrices

1.4VectorInnerProductsandNorms

1.5MatrixNorms

1.6Subspaces,Range,andKernel

1.7OrthogonalVectorsandSubspaces

1.8CanonicalFormsofMatrices

1.8.1ReductiontotheDiagonalForm

1.8.2TheJordanCanonicalForm

1.8.3TheSchurCanonicalForm

1.8.4ApplicationtoPowersofMatrices

1.9NormalandHermitianMatrices

1.9.1NormalMatrices

1.9.2HermitianMatrices

1.10NonnegativeMatrices,M-Matrices

1.11PositiveDefiniteMatrices

1.12ProjectionOperators

1.12.1RangeandNullSpaceofaProjector

1.12.2MatrixRepresentations

1.12.3OrthogonalandObliqueProjectors

1.12.4PropertiesofOrthogonalProjectors

1.13BasicConceptsinLinearSystems

1.13.1ExistenceofaSolution

1.13.2PerturbationAnalysis

Exercises

NotesandReferences

2DiscretizationofPartialDifferentialEquations

2.1PartialDifferentialEquations

2.1.1EllipticOperators

2.1.2TheConvectionDiffusionEquation

2.2FiniteDifferenceMethods

2.2.1BasicApproximations

2.2.2DifferenceSchemesfortheLaplacianOperator

2.2.3FiniteDifferencesforOne-DimensionalProblems

2.2.4UpwindSchemes

2.2.5FiniteDifferencesforTwo-DimensionalProblems

2.2.6FastPoissonSolvers

2.3TheFiniteElementMethod

2.4MeshGenerationandRefinement

2.5FiniteVolumeMethod

Exercises

NotesandReferences

3SparseMatrices

3.1Introduction

……

4BasicIterativeMethods

5ProjectionMethods

6KrylovSubspaceMethods,PartⅠ

7KrylovSubspaceMethods,PartⅡ

8MethodsRelatedtotheNormalEquations

9PreconditionedIterations

10PreconditioningTechniques

11ParallelImplementations

12ParallelPreconditioners

13MultigridMethods

14DomainDecompositionMethods

Bibliography

Index

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