TY - BOOK ID - 8211754 TI - Theoretical numerical analysis : a functional analysis framework AU - Atkinson, Kendall E. AU - Han, Weimin. PY - 2009 SN - 1441931996 1441904573 9786612333187 1282333186 1441904581 PB - New York : Springer, DB - UniCat KW - Functional analysis. KW - Functional analysis KW - Calculus KW - Mathematics KW - Physical Sciences & Mathematics KW - Mathematical analysis. KW - 517.1 Mathematical analysis KW - Mathematical analysis KW - Functional calculus KW - Mathematics. KW - Analysis (Mathematics). KW - Numerical analysis. KW - Analysis. KW - Numerical Analysis. KW - Calculus of variations KW - Functional equations KW - Integral equations KW - Global analysis (Mathematics). KW - Analysis, Global (Mathematics) KW - Differential topology KW - Functions of complex variables KW - Geometry, Algebraic KW - Calculus. KW - Analysis (Mathematics) KW - Fluxions (Mathematics) KW - Infinitesimal calculus KW - Limits (Mathematics) KW - Functions KW - Geometry, Infinitesimal UR - https://www.unicat.be/uniCat?func=search&query=sysid:8211754 AB - 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, boundary integral equations for planar regions, and multivariable polynomial approximations. 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 third edition, a new chapter, Multivariable Polynomial Approximations, is included, numerous changes are made 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. ER -