Best Approximation by Linear Combinations of Characteristic Functions of Half-Spaces

0404318 - UIVT-O 20030003 RIV US eng J - Journal Article
Kainen, P.C. - Kůrková, Věra - Vogt, A.
Best Approximation by Linear Combinations of Characteristic Functions of Half-Spaces.
Journal of Approximation Theory. Roč. 122, č. 2 (2003), s. 151-159. ISSN 0021-9045. E-ISSN 1096-0430
R&D Projects: GA ČR GA201/99/0092; GA ČR GA201/02/0428
Institutional research plan: AV0Z1030915
Keywords : best approximation * proximinal * approximatively compact * boundedly compact * heaviside perceptron networks * plane waves
Subject RIV: BA - General Mathematics
Impact factor: 0.528, year: 2003

It is shown that for any positive integer n and any Lp-function f there exist n half-spaces such that f has a best approximation by a linear combination of their characteristic functions. Further, any sequence of linear combinations of n half-space characteristic functions converging in distance to the best approximation distance has a subsequence converging to a best approximation, i.e., the set of such n-fold linear combinations is an approximatively compact set.
Permanent Link: http://hdl.handle.net/11104/0124577