应用迭代分析（英文版）

图书标准信息

• 作者 袁锦昀 著
• 出版社 科学出版社
• 出版时间 2014-11
• 版次 1
• ISBN 9787030420787
• 定价 98.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 268页
• 字数 300千字
• 正文语种 简体中文
• 丛书 信息与计算科学丛书

【内容简介】

　　袁锦昀教授是杰出的旅居巴西华人1957年出生于江苏兴化唐刘镇，1977年考入南京工学院，巴西巴拉那联邦大学数学系终身教授、工业数学研究所所长，巴西计算和应用数学学会副会长，巴西数学会巴拉那州分会会长，巴西科技部基金委数学终审组应用数学和计算数学负责人，巴西巴拉那基金委数学终身组成员。《实用迭代分析(英文版)(精)》是由其创作的英文版实用迭代分析专著。

【目录】

PrefacetotheSeriesinInformationandComputationalScience
Preface
Chapter1Introduction
1.1Backgroundinlinearalgebra
1.1.1Basicsymbols,notations,anddefinitions
1.1.2Vectornorm
1.1.3Matrixnorm
1.1.4Spectralradii
1.2Spectralresultsofmatrix
1.3Specialmatrices
1.3.1Reducibleandirreduciblematrices
1.3.2Diagonallydominantmatrices
1.3.3Nonnegativematrices
1.3.4p-cyclicmatrices
1.3.5Toeplitz,Hankel,Cauchy,Cauchy-likeandHessenbergmatrices"
1.4Matrixdecomposition
1.4.1LUdecomposition
1.4.2Singularvaluedecomposition
1.4.3Conjugatedecomposition
1.4.4QZdecomposition
1.4.5STdecomposition
1.5Exercises
Chapter2BasicMethodsandConvergence
2.1Basicconcepts
2.2TheJacobimethod
2.3TheGauss-Seidelmethod
2.4TheSORmethod
2.5M-matricesandsplittingmethods
2.5.1M-matrix
2.5.2Splittingmethods
2.5.3Comparisontheorems
2.5.4Multi-splittingmethods
2.5.5GeneralizedOstrowski-Reichtheorem
2.6Erroranalysisofiterativemethods
2.7Iterativerefinement
2.8Exercises
Chapter3Non-stationaryMethods
3.1Conjugategradientmethods
3.1.1Steepestdescentmethod
3.1.2Conjugategradientmethod
3.1.3Preconditionedconjugategradientmethod
3.1.4Generalizedconjugategradientmethod
3.1.5Theoreticalresultsontheconjugategradientmethod
3.1.6GeueuAzedpoduct-tpemethodsbaseu-QC
3.1.7Inexactpreconditionedconjugategradientmethod
3.2Lanczosmethod
3.3GMRESmethodandQMRmethod
3.3.1GMRESmethod
3.3.2QMRmethod
3.3.3VariantsoftheQMRmethod
3.4Directprojectionmethod
3.4.1Theoryofthedirectprojectionmethod
3.4.2Directprojectionalgorithms
3.5Semi-conjugatedirectionmethod
3.5.1Semi-conjugatevectors
3.5.2Leftconjugatedirectionmethod
3.5.3Onepossiblewaytofindleftconjugatevectorset
3.5.4Remedyforbreakdown
3.5.5RelationwithGaussianelimination
3.6Krylovsubspacemethods
3.7Exercises
Chapter4IterativeMethodsforLeastSquaresProblems
4.1Introduction
4.2Basiciterativemethods
4.3BlockSORmethods
4.3.1BlockSORalgorithms
4.3.2Convergenceandoptimalfactors
4.3.3Example
4.4Preconditionedconjugategradientmethods
4.5Generalizedleastsquaresproblems
4.5.1BlockSORmethods
4.5.2Preconditionedconjugategradientmethod
4.5.3Comparison
4.5.4SOR-likemethods
4.6Rankdeficientproblems
4.6.1Augmentedsystemofnormalequation
4.6.2BlockSORalgorithms
4.6.3Convergenceandoptimalfactor
4.6.4Preconditionedconjugategradientmethod
4.6.5Comparisonresults
4.7Exercises
Chapter5Preconditioners
5.1LUdecompositionandorthogonaltransformations
5.1.1GilbertandPeierlsalgorithmforLUdecomposition
5.1.2Orthogonaltransformations
5.2Stationarypreconditioners
5.2.1Jacobipreconditioner
5.2.2SSORpreconditioner
5.3Incompletefactorization
5.3.1Pointincompletefactorization
5.3.2Modifiedincompletefactorization
5.3.3Blockincompletefactorization
5.4Diagonallydominantpreconditioner
5.5Preconditionerforleastsquaresproblems
5.5.1PreconditionerbyLUdecomposition
5.5.2Preconditionerbydirectprojectionmethod
5.5.3PreconditionerbyQRdecomposition
5.6Exercises
Chapter6SingularLinearSystems
6.1Introduction
6.2Propertiesofsingularsystems
6.3Splittingmethodsforsingularsystems
6.4NonstationarymethodsforSingularsystems
6.4.1symmetricandpositivesemidefinitesystems
6.4.2Generalsystems
6.5Exercises
Bibliography
Index