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Other titles in the Cambridge Tracts in Mathematics series:
Cambridge Tracts in Mathematics #93: On L1-Approximationby Allan Pinkus
Synopses & Reviews
This monograph discusses the qualitative linear theory of best LT1-approximation from finite-dimensional subspaces. It presents a survey of recent research that extends "classical" results concerned with best-uniform approximation to the more general case. The work is organized to serve as a self-study guide or as a text for advanced courses. It begins with a basic introduction to the concepts of approximation theory before addressing 1- or 2-sided best approximations from finite-dimensional subspaces and approaches to the computation of these. At the end of each chapter is a series of exercises that give the reader an opportunity to test understanding and also contain some theoretical digressions and extensions of the text.
This monograph is concerned with the qualitative linear 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 more general case.
Table of Contents
Preface; 1. Preliminaries; 2. Approximation from finite-dimensional subspaces of L1; 3. Approximation from finite-dimensional subspaces in C1 (K, µ); 4. Unicity subspaces and property A; 5. One-sided L1-approximation; 6. Discrete lm1 - approximation; 7. Algorithms; Appendices; References; Author index; Subject index.
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