数值分析
作者：Rainer Kress著
出版时间：2003年版
丛编项： Graduate Texts in Mathematics
内容简介
No applied mathematician can be properly trained without some basic understanding of numerical methods， i.e.， numerical analysis. And no scientist and engineer should be using a package program for numerical computations without understanding the program's purpose and its limitations. This book is an attempt to provide some of the required knowledge and understanding. It is written in a spirit that considers numerical analysis not merely as a tool fer solving applied problems but also as a challenging and rewarding part of mathematics. The main goal is to provide insight into numerical analysis rather than merely to provide numerical recipes.此书为英文版！
目录
1Introduction
2LinearSystems
2.1ExamplesforSystemsofEquations
2.2GaussianElimination
2.3LRDecomposition
2.4QRDecomposition
Problems
3BasicFunctionalAnalysis
3.1NormedSpaces
3.2ScalarProducts
3.3BoundedLinearOperators
3.4MatrixNorms
3.5Completeness
3.6TheBanachFixedPointTheorem
3.7BestApproximation
Problems
4IterativeMethodsforLinearSystems
4.1JacobiandGauss-SeidelIterations
4.2RelaxationMethods
4.3Two-GridMethods
Problems
5Ill-ConditionedLinearSystems
5.1ConditionNumber
5.2SingularValueDecomposition
5.3TikhonovRegularization
Problems
6IterativeMethodsforNonlinearSystems
6.1SuccessiveApproximations
6.2Newton'sMethod
6.3ZerosofPolynomials
6.4LeastSquaresProblems
Problems
7MatrixEigenvalueProblems
7.1Examples
7.2EstimatesfortheEigenvalues
7.3TheJacobiMethod
7.4TheQRAlgorithm
7.5HessenbergMatrices
Problems
8Interpolation
8.1PolynomialInterpolation
8.2TrigonometricInterpolation
8.3SplineInterpolation
8.4BezierPolynomials
Problems
9NumericalIntegration
9.1InterpolatoryQuadratures
9.2ConvergenceofQuadratureFormulae
9.3GaussianQuadratureFormulae
9.4QuadratureofPeriodicFunctions
9.5RombergIntegration
9.6ImproperIntegrals
Problems
10InitialValueProblems
10.1ThePicard-LindelSfTheorem
10.2Euler'sMethod
10.3Single-StepMethods
10.4MultistepMethods
Problems
11BoundaryValueProblems
11.1ShootingMethods
11.2FiniteDifferenceMethods
11.3TheRieszandLax-MilgramTheorems
11.4WeakSolutions
11.5TheFiniteElementMethod
Problems
12IntegralEquations
12.1TheRieszTheory
12.2OperatorApproximations
12.3NystrSm'sMethod
12.4TheCollocationMethod
12.5Stability
Problems
References
Index
