Theoretical numerical analysis : a functional analysis framework
 Author/Creator
 Atkinson, Kendall E.
 Language
 English.
 Edition
 3rd ed.
 Imprint
 Dordrecht ; New York : Springer, c2009.
 Physical description
 xvi, 625 p. : ill. ; 25 cm.
 Series
 Texts in applied mathematics ; 39.
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Contributors
 Contributor
 Han, Weimin.
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Linear Spaces. Linear Operators on Normed Spaces. Approximation Theory. Fourier Analysis and Wavelets. Nonlinear Equations and Their Solution by Iteration. Finite Difference Method. Sobolev Spaces. Weak Formulations of Elliptic Boundary Value Problems. The Galerkin Method and Its Variants. Finite Element Analysis. Elliptic Variational Inequalities and Their Numerical Approximations. Numerical Solution of Fredholm Integral Equations of the Second Kind. Boundary Integral Equations. Multivariable Polynomial Approximations.
 (source: Nielsen Book Data)
 Publisher's Summary
 This textbook prepares graduate students for research in numerical analysis/computational mathematics by giving to them a mathematical framework embedded in functional analysis and focused on numerical analysis. This helps the student to move rapidly into a research program. The text covers basic results of functional analysis, approximation theory, Fourier analysis and wavelets, iteration methods for nonlinear equations, finite difference methods, Sobolev spaces and weak formulations of boundary value problems, finite element methods, elliptic variational inequalities and their numerical solution, numerical methods for solving integral equations of the second kind, and boundary integral equations for planar regions. The presentation of each topic is meant to be an introduction with certain degree of depth. Comprehensive references on a particular topic are listed at the end of each chapter for further reading and study. Because of the relevance in solving real world problems, multivariable polynomials are playing an ever more important role in research and applications. In this third editon, a new chapter on this topic has been included and some major changes are made on two chapters from the previous edition. In addition, there are numerous minor changes throughout the entire text and new exercises are added. Review of earlier edition: "...the book is clearly written, quite pleasant to read, and contains a lot of important material; and the authors have done an excellent job at balancing theoretical developments, interesting examples and exercises, numerical experiments, and bibliographical references." R. Glowinski, SIAM Review, 2003.
(source: Nielsen Book Data)
Subjects
 Subject
 Functional analysis.
Bibliographic information
 Publication date
 2009
 Responsibility
 Kendall Atkinson, Weimin Han.
 Series
 Texts in applied mathematics ; 39
 ISBN
 9781441904577
 1441904573