On L1-Approximation

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Paperback | 15 May 2008

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252 Pages

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This monograph is concerned with the qualitative theory of best L1-approximation from finite-dimensional subspaces. It presents a survey of recent research that extends 'classical' results concerned with best uniform approximation to the L1 case. The work is organized in such a way as to be useful for self-study or as a text for advanced courses. It begins with a basic introduction to the concepts of approximation theory before addressing one- or two-sided best approximation from finite-dimensional subspaces and approaches to the computation of these. At the end of each chapter is a series of exercises; these give the reader an opportunity to test understanding and also contain some theoretical digressions and extensions of the text.

Industry Reviews

"A clearly written, friendly, and enthusiastic introduction to the qualitative theory of best approximation..." American Mathematical Monthly "...an excellent compendium of the current best known qualitative results on best approximations from finite-dimensional subspaces of L1 spaces...could easily be used in a graduate topics course, and surely will be a standard reference work." Mathematical Reviews

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Preface
Preliminaries
Approximation from finite-dimensional subspaces of L1
Approximation from finite-dimensional subspaces in C1 (K, )
Unicity subspaces and property A
One-sided L1-approximation
Discrete lm1 - approximation
Algorithms
Appendices
References
Author index
Subject index
Table of Contents provided by Publisher. All Rights Reserved.

On L1-Approximation

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