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  • 理论数值分析(第3版)[平装]
  • 共4个商家     78.40元~87.10
  • 作者:K.阿特肯森(KendallAtkinson)(作者)
  • 出版社:世界图书出版公司北京公司;第1版(2013年1月1日)
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  • ISBN:9787510052781

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    《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。

    作者简介

    作者:(美国)阿特肯森(Atkinson K. )

    目录

    Series Preface
    Preface
    Linear Spaces
    1.1 Linear spaces
    1.2 Normed spaces
    1.2.1 Convergence
    1.2.2 Banach spaces
    1.2.3 Completion of normed spaces
    1.3 Inner product spaces
    1.3.1 Hilbert spaces
    1.3.2 Orthogonality
    1.4 Spaces of continuously differentiable functions
    1.4.1 HSlder spaces
    1.5 Lp spaces
    1.6 Compact sets
    Linear Operators on Normed Spaces
    2.1 Operators
    2.2 Continuous linear operators
    2.2.1 (V,W) as a Banach space
    2.3 The geometric series theorem and its variants
    2.3.1 A generalization
    2.3.2 A perturbation result
    2.4 Some more results on linear operators
    2.4.1 An extension theorem
    2.4.2 Open mapping theorem
    2.4.3 Principle of uniform boundedness
    2.4.4 Convergence of numerical quadratures
    2.5 Linear functionals
    2.5.1 An extension theorem for linear functionals
    2.5.2 The Riesz representation theorem
    2.6 Adjoint operators
    2.7 Weak convergence and weak compactness
    2.8 Compact linear operators
    2.8.1 Compact integral operators on C(D)
    2.8.2 Properties of compact operators
    2.8.3 Integral operators on L2(a,b)
    2.8.4 The Fredholm alternative theorem
    2.8.5 Additional results on Fredholm integral equations
    2.9 The resolvent operator
    2.9.1 R(A) as a holomorphic function
    Approximation Theory
    3.1 Approximation of continuous functions by polynomials
    3.2 Interpolation theory
    3.2.1 Lagrange polynomial interpolation
    3.2.2 Hermite polynomial interpolation
    3.2.3 Piecewise polynomial interpolation
    3.2.4 Trigonometric interpolation
    3.3 Best approximation
    3.3.1 Convexity,lower semicontinuity
    3.3.2 Some abstract existence results
    3.3.3 Existence of best approximation
    3.3.4 Uniqueness of best approximation
    3.4 Best approximations in inner product spaces,projection on
    closed convex sets
    3.5 Orthogonal polynomials
    3.6 Projection operators
    3.7 Uniform error bounds
    3.7.1 Uniform error bounds for L2-approximations
    3.7.2 L2-approximations using polynomials
    3.7.3 Interpolatory projections and their convergence
    Fourier Analysis and Wavelets
    4.1 Fourier series
    4.2 Fourier transform
    4.3 Discrete Fourier transform
    4.4 Haar wavelets
    4.5 Multiresolution analysis
    Nonlinear Equations and Their Solution by Iteration
    5.1 The Banach fixed-point theorem
    5.2 Applications to iterative methods
    5.2.1 Nonlinear algebraic equations
    5.2.2 Linear algebraic systems
    5.2.3 Linear and nonlinear integral equations
    5.2.4 Ordinary differential equations in Banach spaces
    5.3 Differential calculus for nonlinear operators
    5.3.1 Frechet and Gateaux derivatives
    5.3.2 Mean value theorems
    5.3.3 Partial derivatives
    5.3.4 The Gateaux derivative and convex minimization
    5.4 Newton's method
    5.4.1 Newton's method in Banach spaces
    5.4.2 Applications
    5.5 Completely continuous vector fields
    5.5.1 The rotation of a completely continuous vector field
    5.6 Conjugate gradient method for operator equations
    Finite Difference Method
    6.1 Finite difference approximations
    6.2 Lax equivalence theorem
    6.3 More on convergence
    Sobolev Spaces
    7.1 Weak derivatives
    7.2 Sobolev spaces
    7.2.1 Sobolev spaces of integer order
    7.2.2 Sobolev spaces of real order
    7.2.3 Sobolev spaces over boundaries
    7.3 Properties
    7.3.1 Approximation by smooth functions
    7.3.2 Extensions
    7.3.3 Sobolev embedding theorems
    7.3.4 Traces
    7.3.5 Equivalent norms
    7.3.6 A Sobolev quotient space
    7.4 Characterization of Sobolev spaces via the Fourier transform
    7.5 Periodic Sobolev spaces
    7.5.1 The dual space
    7.5.2 Embedding results
    7.5.3 Approximation results
    7.5.4 An illustrative example of an operator
    7.5.5 Spherical polynomials and spherical harmonics
    7.6 Integration by parts formulas
    8 Weak Formulations of Elliptic Boundary Value Problems
    8.1 A model boundary value problem
    8.2 Some general results on existence and uniqueness
    8.3 The Lax-Milgram Lemma
    8.4 Weak formulations of linear elliptic boundary value problems
    8.4.1 Problems with homogeneous Dirichlet boundary con-ditions
    8.4.2 Problems with non-homogeneous Dirichlet boundary conditions
    8.4.3 Problems with Neumann boundary conditions
    8.4.4 Problems with mixed boundary conditions
    8.4.5 A general linear second-order elliptic boundary value problem
    8.5 A boundary value problem of linearized elasticity
    8.6 Mixed and dual formulations
    8.7 Generalized Lax-Milgram Lemma
    8.8 A nonlinear problem
    9 The Galerkin Method and Its Variants
    9.1 The Galerkin method
    9.2 The Petrov-Galerkin method
    9.3 Generalized Galerkin method
    9.4 Conjugate gradient method: variational formulation
    10 Finite Element Analysis
    10.1 One-dimensional examples
    10.1.1 Linear elements for a second-order problem
    10.1.2 High order elements and the condensation technique
    10.1.3 Reference element technique
    10.2 Basics of the finite element method
    10.2.1 Continuous linear elements
    10.2.2 Affine-equivalent finite elements
    10.2.3 Finite element spaces
    10.3 Error estimates of finite element interpolations
    10.3.1 Local interpolations
    10.3.2 Interpolation error estimates on the reference element
    10.3.3 Local interpolation error estimates
    10.3.4 Global interpolation error estimates
    10.4 Convergence and error estimates
    ……
    11 Elliptic Variational Inequalities and Their Numerical Ap-proximations
    12 Numerical Solution of Fredholm Integral Equations of the Second Kind
    13 Boundary Integral Equations
    14 Multivariable Polynomial Approximations
    References
    Index

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