Continuous Selections for Metric Projections and Interpolating Subspaces
Published on 1. February 1991
Book
Paperback/Softback
II, 114 pages
978-3-631-43521-2 (ISBN)
Description
The existence of continuous selections for metric projections is the theoretical foundation of the existence of stable algorithms for computing best approximation elements. In this monograph we will give various intrinsic characterizations of subspaces of C o(T) which ensure the existence of continuous metric selections. Since the Chebyshev approximation is a special case of semi-infinite optimization, we hope that our study will give some insight to stability problems in semi-infinite optimization as well as parametric optimizations.
Reviews / Votes
«We warmly recommend this book to all specialists working in this area.» (S.S. Dragomir, Zentralbaltt für Mathematik und ihre Grenzgebiete)«The book can be recommended for graduate courses on approximation theory and surely will be a valuable refernce work.» (Manfred Sommer, Mathematical Reviews)
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Content
Contents: This monograph deals with various intrinsic characterizations of those subspaces G of C o(T) whose metric projections P G have continuous selections. We have a systematic development of the theory of the classical Chebyshev alternation phenomena and the strict best approximation introduced by J.R. Rice.