On L1-Approximation [Hardcover]

This monograph is concerned with the qualitative theory of best L1-approximation from finite-dimensional subspaces.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.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.This monograph discusses the qualitative linear theory of best L^T1-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.Preface; 1. Preliminaries; 2. Approximation from finite-dimensional subspaces of L1; 3. Approximation from finite-dimensional subspaces in C1 (K, ?); 4. Unicity subspaces and property A; 5. One-sided L1-approximation; 6. Discrete lm1 - approximation; 7. Algorithms; Appendices; References; Author index; Subject index. A clearly written, friendly, and enthusiastic introduction to the qualitative theory of best approximation... American Mathematicl£Ù