Exact Constants in Approximation Theory
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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.
Reviews & endorsements
"...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 ReviewsSee more 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
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- Date Published: July 2013
- format: Adobe eBook Reader
- isbn: 9781107108226
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
1. Best approximation and duality in extremal problems
2. Polynomials and spline-functions as approximating tools
3. Comparison theorems and inequalities for the norms of functions and their derivatives
4. Polynomial approximation of classes of functions with bounded r-th derivative in Lp
5. Spline approximation of classes of functions with bounded r-th derivative
6. Exact constants in Jackson inequalities
7. Approximation of classes of functions determined by modulus of continuity
8. N-widths of functional classes and closely related extremal problems
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