Exact constants in approximation theory
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 rela...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Cambridge
Cambridge University Press
1990
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| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 38 |
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| Online-Zugang: | DE-12 DE-92 URL des Erstveröffentlichers |
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| 520 | |a 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 | ||
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Datensatz im Suchindex
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| author | Korneĭchuk, Nikolaĭ Pavlovich |
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| dewey-full | 511/.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
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| dewey-search | 511/.4 |
| dewey-sort | 3511 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781107325791 |
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| id | DE-604.BV043941576 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-24T05:33:59Z |
| institution | BVB |
| isbn | 9781107325791 |
| language | English |
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| series2 | Encyclopedia of mathematics and its applications |
| spelling | Korneĭchuk, Nikolaĭ Pavlovich Verfasser aut Tochnye konstanty v teorii priblizhenii͡a Exact constants in approximation theory N. Korneichuk ; translated from the Russian by K. Ivanov Cambridge Cambridge University Press 1990 1 online resource (xii, 452 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 38 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 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 Approximation theory Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Approximationstheorie (DE-588)4120913-8 s 1\p DE-604 Ivanov, K. trl Erscheint auch als Druckausgabe 978-0-521-11156-0 Erscheint auch als Druckausgabe 978-0-521-38234-2 https://doi.org/10.1017/CBO9781107325791 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Korneĭchuk, Nikolaĭ Pavlovich Exact constants in approximation theory Approximation theory Approximationstheorie (DE-588)4120913-8 gnd |
| subject_GND | (DE-588)4120913-8 |
| title | Exact constants in approximation theory |
| title_alt | Tochnye konstanty v teorii priblizhenii͡a |
| title_auth | Exact constants in approximation theory |
| title_exact_search | Exact constants in approximation theory |
| title_full | Exact constants in approximation theory N. Korneichuk ; translated from the Russian by K. Ivanov |
| title_fullStr | Exact constants in approximation theory N. Korneichuk ; translated from the Russian by K. Ivanov |
| title_full_unstemmed | Exact constants in approximation theory N. Korneichuk ; translated from the Russian by K. Ivanov |
| title_short | Exact constants in approximation theory |
| title_sort | exact constants in approximation theory |
| topic | Approximation theory Approximationstheorie (DE-588)4120913-8 gnd |
| topic_facet | Approximation theory Approximationstheorie |
| url | https://doi.org/10.1017/CBO9781107325791 |
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