On L1-Approximation

This monograph is concerned with the qualitative theory of best L1-approximation from finite-dimensional subspaces.

Allan M. Pinkus (Author)

9780521057691, Cambridge University Press

Paperback / softback, published 28 January 2008

252 pages
23 x 15.3 x 1.5 cm, 0.416 kg

"...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

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.

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.

Subject Areas: Numerical analysis [PBKS]