理论数值分析（第3版）

图书标准信息

• 作者 [美]阿特肯森（Atkinson,K.） 著
• 出版社 世界图书出版公司
• 出版时间 2013-01
• 版次 3
• ISBN 9787510052781
• 定价 99.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 625页
• 正文语种 英语

【内容简介】

　　《理论数值分析（第3版）》旨在为读者提供一个基于泛函分析并专注于数值分析的数学框架，让读者更好地学习数值分析和计算数学，及早进入科研项目。本教程包括了泛函分析、逼近理论、傅里叶分析和小波等诸多基础专题，每个专题的表述既能了解该科目，又可以达到一定的深度，特别专题的参考文献都列于每章末，供读者深入学习和研究。由于现实问题的往往是多相关的，多变量多项式在研究和应用中扮演着重要的角色，第三版中就此专题新增了一章。

【目录】

SeriesPreface
Preface

1LinearSpaces
1.1Linearspaces
1.2Normedspaces
1.2.1Convergence
1.2.2Banachspaces
1.2.3Completionofnormedspaces
1.3Innerproductspaces
1.3.1Hilbertspaces
1.3.2Orthogonality
1.4Spacesofcontinuouslydifferentiablefunctions
1.4.1HSlderspaces
1.5Lpspaces
1.6Compactsets

2LinearOperatorsonNormedSpaces
2.1Operators
2.2Continuouslinearoperators
2.2.1C（V,W）asaBanachspace
2.3Thegeometricseriestheoremanditsvariants
2.3.1Ageneralization
2.3.2Aperturbationresult
2.4Somemoreresultsonlinearoperators
2.4.1Anextensiontheorem
2.4.2Openmappingtheorem
2.4.3Principleofuniformboundedness
2.4.4Convergenceofnumericalquadratures
2.5Linearfunctionals
2.5.1Anextensiontheoremforlinearfunctionals
2.5.2TheRieszrepresentationtheorem
2.6Adjointoperators
2.7Weakconvergenceandweakcompactness
2.8Compactlinearoperators
2.8.1CompactintegraloperatorsonC（D）
2.8.2Propertiesofcompactoperators
2.8.3IntegraloperatorsonL2（a,b）
2.8.4TheFredholmalternativetheorem
2.8.5AdditionalresultsonFredholmintegralequations
2.9Theresolventoperator
2.9.1R（r）asaholomorphicfunction

3ApproximationTheory
3.1Approximationofcontinuousfunctionsbypolynomials
3.2Interpolationtheory
3.2.1Lagrangepolynomialinterpolation
3.2.2Hermitepolynomialinterpolation
3.2.3Piecewisepolynomialinterpolation
3.2.4Trigonometricinterpolation
3.3Bestapproximation
3.3.1Convexity,lowersemicontinuity
3.3.2Someabstractexistenceresults
3.3.3Existenceofbestapproximation
3.3.4Uniquenessofbestapproximation
3.4Bestapproximationsininnerproductspaces,projectionorclosedconvexsets
3.5Orthogonalpolynomials
3.6Projectionoperators
3.7Uniformerrorbounds
3.7.1UniformerrorboundsforL2-approximations
3.7.2L2-approximationsusingpolynomials
3.7.3Interpolatoryprojectionsandtheirconvergence

4FourierAnalysisandWavelets
4.1Fourierseries
4.2Fouriertransform
4.3DiscreteFouriertransform
4.4Haarwavelets
4.5Multiresolutionanalysis

5NonlinearEquationsandTheirSolutionbyIteration
6FiniteDifferenceMethod
7SobolevSpaces
8WeakFormulationsofEllipticBoundaryValueProblems
9TheGalerkinMethodandItsVariants
10FiniteElementAnalysis
11EllipticVariationalInequalitiesandTheirNumericalApproximations
12NumericalSolutionofFredholmIntegralEquationsoftheSecondKind
13BoundaryIntegralEquations
14MultivariablePolynomialApproximations
References
Index