Exact Constants in Approximation Theory (Hardcover)

Nikolai Pavlovich Korneichuk

ISBN 10: 0521382343 / ISBN 13: 9780521382342

Published by Cambridge University Press, Cambridge, 1991

About this Item

Hardcover. This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are based on deep facts from analysis and function theory, such as duality theory and comparison theorems; these are presented in chapters 1 and 3. In keeping with the author's intention to make the book as self-contained as possible, chapter 2 contains an introduction to polynomial and spline approximation. Chapters 4 to 7 apply the theory to specific classes of functions. The last chapter deals with n-widths and generalises some of the ideas of the earlier chapters. Each chapter concludes with commentary, exercises and extensions of results. A substantial bibliography is included. Many of the results collected here have not been gathered together in book form before, so it will be essential reading for approximation theorists. This book is a self-contained introduction to the particular area of approximation theory concerned with exact constants; the results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; and optimal reconstruction of functions and linear functionals. Many of the results are based on facts from analysis and function theory, such as duality theory and comparison theorems. Each chapter concludes with commentary, exercises, and extensions of results, and a substantial bibliography is also included. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Seller Inventory # 9780521382342

Bibliographic Details

Title: Exact Constants in Approximation Theory (...

Publisher: Cambridge University Press, Cambridge

Publication Date: 1991

Binding: Hardcover

Condition: new

About this title

Synopsis:

This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are based on deep facts from analysis and function theory, such as duality theory and comparison theorems; these are presented in chapters 1 and 3. In keeping with the author's intention to make the book as self-contained as possible, chapter 2 contains an introduction to polynomial and spline approximation. Chapters 4 to 7 apply the theory to specific classes of functions. The last chapter deals with n-widths and generalises some of the ideas of the earlier chapters. Each chapter concludes with commentary, exercises and extensions of results. A substantial bibliography is included. Many of the results collected here have not been gathered together in book form before, so it will be essential reading for approximation theorists.

Review:

"...a good summary of the Russian literature in the area and would be (especially the bibliography) useful to workers in approximation theory who encounter best constant problems." Terence M. Mills, Mathematical Reviews

"...will be useful to mathematicians who work in approximation theory and are interested in best-constant questions...some people who work in numerical analysis or computational mathematics may also be interested in it." T.M. Mills, The Mathematical Intelligencer