国外数学名著系列（续1）（影印版）39：稀疏线性系统的迭代方法（第2版）

图书标准信息

• 作者 [美]萨阿德 著
• 出版社 科学出版社
• 出版时间 2009-01
• 版次 2
• ISBN 9787030234834
• 定价 98.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 528页
• 字数 665千字
• 正文语种 英语

【内容简介】

《国外数学名著系列（续1）（影印版）39：稀疏线性系统的迭代方法（第2版）》canbeusedtoteachgraduate-levelcoursesoniterativemethodsforlinearsystems.Engineersandmathematicianswillfinditscontentseasilyaccessible，andpractitionersandeducatorswillvalueitasahelpfulresource.Theprefaceincludessyllabithatcanbeusedforeitherasemester-orquarter-lengthcourseinbothmathematicsandcomputerscience.IterativeMethodsforSparseLinearSystems，SecondEditiongivesanin-depth，up-to-dateviewofpracticalalgorithmsforsolvinglarge-scalelinearsystemsofequations.Theseequationscannumberinthemillionsandaresparseinthesensethateachinvolvesonlyasmallnumberofunknowns.Themethodsdescribedareiterative，i.e.，theyprovidesequencesofapproximationsthatwillconvergetothesolution.
Thisneweditionincludesawiderangeofthebestmethodsavailabletoday.Theauthorhasaddedanewchapteronmultigridtechniquesandhasupdatedmaterialthroughoutthetext，particularlythechaptersonsparsematrices，Krylovsubspacemethods，preconditioningtechniques，andparallelpreconditioners.Materialonoldertopicshasbeenremovedorshortened，numerousexerciseshavebeenadded，andmanytypographicalerrorshavebeencorrected.Theupdatedandexpandedbibliographynowincludesmorerecentworksemphasizingnewandimportantresearchtopicsinthisfield.

【目录】

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-DimensionalProblerr
2.2.4UpwindSchemes
2.2.5FiniteDifferencesforTwo-DimensionalProblerr
2.2.6FastPoissonSolvers
2.3TheFiniteElementMethod
2.4MeshGenerationandRefinement
2.5FiniteVolumeMethod
Exercises
NotesandReferences

3SparseMatrices
3.1Introduction
3.2GraphRepresentations
3.2.1GraphsandAdjacencyGraphs
3.2.2GraphsofPDEMatrices
3.3PermutationsandReorderings
3.3.1BasicConcepts
3.3.2RelationswiththeAdjacencyGraph
3.3.3CommonReorderings
3.3.4Irreducibility
3.4StorageSchemes
3.5BasicSparseMatrixOperations
3.6SparseDirectSolutionMethods
3.6.1MDOrdering
3.6.2NDOrdering
3.7TestProblems
Exercises
NotesandReferences

4BasicIterativeMethods
4.1Jacobi，Gauss-Seidel，andSuccessiveOverrelaxation
4.1.1BlockRelaxationSchemes
4.1.2IterationMatricesandPreconditioning
4.2Convergence
4.2.1GeneralConvergenceResult
4.2.2RegularSplittings
4.2.3DiagonallyDominantMatrices
4.2.4SymmetricPositiveDefiniteMatrices
4.2.5PropertyAandConsistentOrderings
4.3AlternatingDirectionMethods
Exercises
NotesandReferences

5ProjectionMethods
5.1BasicDefinitionsandAlgorithms
5.1.1GeneralProjectionMethods
5.1.2MatrixRepresentation
5.2GeneralTheory
5.2.1TwoOptimalityResults
5.2.2InterpretationinTermsofProjectors
5.2.3GeneralErrorBound
5.3One-DimensionalProjectionProcesses
5.3.1SteepestDescent
5.3.2MRIteration
5.3.3ResidualNormSteepestDescent
5.4AdditiveandMultiplicativeProcesses
Exercises
NotesandReferences

6KryiovSubspaceMethods，PartI
6.1Introduction
6.2KrylovSubspaces
6.3ArnoldisMethod
6.3.1TheBasicAlgorithm
6.3.2PracticalImplementations
6.4ArnoldisMethodforLinearSystems
6.4.1Variation1：RestartedFOM
6.4.2Variation2：IOMandDIOM
6.5GeneralizedMinimalResidualMethod
6.5.1TheBasicGMRESAlgorithm
6.5.2TheHouseholderVersion
6.5.3PracticalImplementationIssues
6.5.4BreakdownofGMRES
6.5.5Variation1：Restarting
6.5.6Variation2：TruncatedGMRESVersions
6.5.7RelationsBetweenFOMandGMRES
6.5.8ResidualSmoothing
6.5.9GMRESforComplexSystems
6.6TheSymmetricLanczosAlgorithm
6.6.1TheAlgorithm
6.6.2RelationtoOrthogonalPolynomials
6.7TheConjugateGradientAlgorithm
6.7.1DerivationandTheory"
6.7.2AlternativeFormulations
6.7.3EigenvalueEstimatesfromtheCGCoefficients
6.8TheConjugateResidualMethod
6.9GeneralizedConjugateResidual，ORTHOMIN，andORTHODIR
6.10TheFaber-ManteuffelTheorem
6.11ConvergenceAnalysis
6.11.1RealChebyshevPolynomials
6.11.2ComplexChebyshevPolynomials
6.11.3ConvergenceoftheCGAlgorithm
6.11.4ConvergenceofGMRES
6.12BlockKrylovMethods
Exercises
NotesandReferences

7KryiovSubspaeeMethods，PartII
7.1LanczosBiorthogonalization
7.1.1TheAlgorithm
7.1.2PracticalImplementations
7.2TheLanczosAlgorithmforLinearSystems
7.3TheBiconjugateGradientandQuasi-MinimalResidualAlgorithms
7.3.1TheBCGAlgorithm
7.3.2QMRAlgorithm
7.4Transpose-FreeVariants
7.4.1CGS
7.4.2BICGSTAB
7.4.3TFQMR
Exercises
NotesandReferences

8MethodsRelatedtotheNormalEquations
8.1TheNormalEquations
8.2RowProjectionMethods
8.2.1Gauss-SeidelontheNormalEquations
8.2.2CimminosMethod
8.3ConjugateGradientandNormalEquations
8.3.1CGNR
8.3.2CGNE
8.4Saddle-PointProblems
Exercises
NotesandReferences

9PreconditionedIterations
9.1Introduction
9.2PreconditionedConjugateGradient
9.2.1PreservingSymmetry
9.2.2EfficientImplementations
……
10PreconditioningTechniques
11ParallelImplementations
12ParallelPreconditioners
13MultigridMethods
14DomainDecompositionMethods
Bibliography
Index