Best approximation by linear combinations of characteristic functions of half-spaces

JOURNAL OF APPROXIMATION THEORY

卷:122

Article

Kainen, PC ; Kurková, V ; Vogt, A

关键词: best approximation;    proximinal;    approximatively compact;    boundedly compact;    heaviside perceptron networks;    plane waves;   

DOI  :  10.1016/S0021-9045(03)00072-8

来源: Elsevier

【 摘 要 】

It is shown that for any positive integer n and any function f in L-p ([0, 1](d)) with p is an element of [ 1, infinity) there exist it 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. (C) 2003 Published by Elsevier Science (USA).

【 授权许可】

Free