国外数学名著系列：矩阵迭代分析（第2版）（影印版）

图书标准信息

• 作者 [美]瓦尔加 著
• 出版社 科学出版社
• 出版时间 2006-01
• 版次 1
• ISBN 9787030166746
• 定价 66.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 372页
• 字数 439千字

【内容简介】

　　《矩阵迭代分析(第二版)》的作者现任英国肯特大学教授，多种国际权威杂志主编或编委。本书第一版1962年由PrenticeHall出版，是矩阵迭代分析方面的经典教材。此次修订，有些章节吸收了新的研究成果，如弱正则分裂方面的结果；有些章节则增添了新的内容，引述了最近的定理，更新了参考文献，读者从中可以了解一些最新的发展方向。此次修订，新的章节的内容基本上都是自含的，并添加了习题。原版主要基于线性代数方法，而修订版强调借助其他领域的工具，如逼近论和共型映射理论，得到更加新颖的结果。本书尤其适合从事数值分析的科研人员和研究生阅读。

【目录】

1.MatrixPropertiesandConcepts
1.1Introduction
1.2ASimpleExample
1.3NormsandSpectralRadii
1.4BoundsfortheSpectralRadiusofaMatrixandDirectedGraphs
1.5DiagonallyDominantMatrices
1.6OvalsofCassini
2.NonnegativeMatrices
2.1SpectralRadiiofNonnegativeMatrices
2.2CyclicandPrimitiveMatrices
2.3ReducibleMatrices
2.4NonnegativeMatricesandDirectedGraphs
3.BasicIterativeMethodsandComparisonTheorems
3.1ThePointJacobi,Gauss-Seidel,andSuccessiveOverrelaxationIterativeMethods
3.2AverageRatesofConvergence
3.3TheStein-RosenbergTheorem
3.4TheOstrowski-ReichTheorem
3.5StieltjesMatrices,M-MatricesandH-Matrices
3.6RegularandWeakRegularSplittingsofMatrices
4.SuccessiveOverrelaxationIterativeMethods
4.1p-CyclicMatrices
4.2TheSuccessiveOverrelaxationIterativeMethodforp-CyclicMatrices
4.3TheoreticalDeterminationofanOptimumRelaxationFactor
4.4Extensionsofthe2-CyclicTheoryofMatrices
4.5AsymptoticRatesofConvergence
4.6CO(q,r)andGCO(q,r):GeneralizedConsistentOrderings
5.Semi-IterativeMethods
5.1Semi-IterativeMethodsandChebyshevPolynomials
5.2RelationshipofSemi-IterativeMethodstoSuccessiveOverrelaxationIterativeMethods
5.3ComparisonofAverageRatesofConvergence:theWeaklyCyclicCase
5.4CyclicReductionandRelatedIterativeMethods
5.5Semi-IterativeMethodsAppliedtotheSuccessiveOverrelaxationMethod
6.DerivationandSolutionofEllipticDifferenceEquations
6.1ASimpleTwo-Pointboundary-ValueProblem
6.2GeneralSecond-OrderOrdinaryDifferentialEquations
6.3DerivationofFiniteDifferenceApproximationsinHigherDimensions
6.4FactorizationTechniquesandblockIterativeMethods
6.5AsymptoticConvergenceRatesfortheModelProblem
7.Alternating-DirectionImplicitIterativeMethods
7.1ThePeaceman-RachfordIterativeMethod
7.2TheCommutativeCase
7.3TheNoncommutativeCase
7.4VariantsofthePeaceman-RachfordIterativeMethod
8.MatrixMethodsforParabolicPartialDifferentialEquations
8.1Semi-DiscreteApproximation
8.2EssentiallyPositiveMatrices
8.3MatrixApproximationsforexp(-tS)
8.4RelationshipwithIterativeMetholdsforSolvingEllipticDifferenceEquations
8.5ChebyshevRationalApproximationsforexp(-tS)
9.EstimationofAccelerationParameters
9.1ApplicationoftheTheoryofNonnegativeMatrices
9.2ApplicationofIsoperimetricInequalities
A.Appendix
B.Appendix
References
Index