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Theoretical Numerical Analy...
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. In this new edition many sections from the first edition have been revised to varying degrees as well as over 140 new exercises added. A new chapter on Fourier Analysis and wavelets has been included. 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
Monografía
monografia Rebiun14443473 https://catalogo.rebiun.org/rebiun/record/Rebiun14443473 cr nn 008mamaa 100301s2005 xxu| s |||| 0|eng d 9780387287690 978-0-387-28769-0 10.1007/978-0-387-28769-0 doi UPVA 996894894103706 CUNEF 991000429462708131 CBUC 991004009409406713 CBUC 991004950316306711 CBUC 991000728322206712 CBUC 991003547825506714 CBUC 991010405710106709 UR0256901 UAM 991007839479404211 CBUC 991008369099706706 CBUC 991005018309706708 PBK bicssc MAT034000 bisacsh Atkinson, Kendall Theoretical Numerical Analysis Recurso electrónico] A Functional Analysis Framework by Kendall Atkinson, Weimin Han New York, NY Springer New York 2005 New York, NY New York, NY Springer New York XVIII, 576 p. 33 illus. digital XVIII, 576 p. 33 illus. Texts in Applied Mathematics 0939-2475 39 Preface to the Second Edition -- Preface to the First Edition -- 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 -- Variational 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 -- References -- Index. Acceso restringido a miembros de la UGR 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. In this new edition many sections from the first edition have been revised to varying degrees as well as over 140 new exercises added. A new chapter on Fourier Analysis and wavelets has been included. 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 Mathematics Global analysis (Mathematics) Numerical analysis Mathematics Analysis Numerical Analysis Han, Weimin SpringerLink (Online service) SpringerLink ebooks (Servicio en línea) Springer eBooks Springer eBooks Printed edition 9780387258874 Texts in Applied Mathematics 0939-2475 39