《Toeplitz系統預處理方法》

《Toeplitz系統預處理方法》是由金小慶著作、高等教育出版社出版的書籍。

基本信息

• 名稱：《Toeplitz系統預處理方法》
• 價格：25.00元
• ISBN：9787040295320
• 開本：16開
• 出版時間：2010年3月1日
• 裝幀：平裝

圖書信息

書名:Toeplitz系統預處理方法
作　者：金小慶　
出版社：高等教育出版社
出版時間：2010-3-1

Toeplitz系統預處理方法

ISBN:9787040295320
開本：16開
定價:25.00元

內容簡介

TheuseofthepreconditionedconjugategradientmethodwithcirculantpreconditionerstosolveToeplitzsystemswasproposedin1986.Inthisshortbook,theauthormainlystudiessomewell-knownpreconditionersfromatheoreticalviewpoint.Anapplicationofpreconditionerstosystemsofordinarydifferentialequationsisalsodiscussed.ThebookcontainsseveralimportantresearchresultsoniterativeToeplitzsolversobtainedinrecentyears.Itcouldbeaccessibletoseniorundergraduatestudentswho,invariousscientificcomputingdisciplines,haveabasiclinearalgebra,calculus,numericalanalysis,andcomputingknowledge.Thebookisalsousefultoresearchersandcomputational'practitionerswhoareinterestedinfastiterativeToeplitzsolvers.
Dr.Xiao-QingJinisaProfessorattheDepartmentofMathematics,UniversityofMacau.Heistheauthorof4booksandover70researchpapers.HeisalsoamemberoftheeditorialbeardsofJournalonNumericalMethodsandComputerApplications,NumericalMathematics:Theory,MethodsandApplications,andEastAsiaJournalofAppliedMathematics.

圖書目錄

1Introduction
1.1Backgroundinnumericallinearalgebra
1.1.1Basicsymbols,notations,anddefinitions
1.1.2SpectralpropertiesofHermitianmatrix
1.1.3Normsandconditionnumber
1.2Toeplitzsystems
1.3Conjugategradientmethod
1.4GMRESmethod
1.5BasicknowledgeofiterativeToeplitzsolvers
1.5.1Circulantpreconditioners
1.5.2Generatingfunctionandspectralanalysis
2Strang'sCirculantPreconditioner
2.1Introduction
2.2Convergencerate
3T.Chan'sOptimalPreconditioner
3.1Introduction
3.2Convergencerate
3.3Non-circulantoptimalpreconditioners
3.3.1Optimalsinetransformpreconditioner
3.3.2Optimalcosinetransformpreconditioner
3.3.3OptimalHartleytransformpreconditioner
3.3.4Convergenceresultandoperationcost
3.4Linearoperatorcu
3.5Stability
4SuperoptimalPreconditioner
4.1Introduction
4.2Convergencerate
4.3Spectralrelationofpreconditionedmatrices
4.4Numericalresults
5Ill-ConditionedToeplitzSystems
5.1Band-Toeplitzpreconditioner
5.2{w}-circulantpreconditioner
5.2.1Constructionofpreconditioner
5.2.2Spectralanalysis
6BlockPreconditioner
6.1Blockoperator■
6.2Complexityofpreconditionedsystem
6.3Convergencerate
6.4Numericalresults
7ApplicationinODEs
7.1BackgroundofBVMs
7.1.1Linearmultistepformulas
7.1.2Block-BVMsandtheirmatrixforms
7.2Constructionofpreconditioner
7.3Convergencerateandoperationcost
7.4Numericalresults
AM-filesusedinChapter7
A.1
A.2
A.3
A.4
A.5
Bibliography
Index