On L1-Approximation
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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 organised 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 ...
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 organised 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.
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.
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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