Journal
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
Volume 341, Issue 4, Pages 391-399Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jfranklin.2004.03.001
Keywords
distance-minimizing sequence; well-posedness; approximative compactness; proximinal set; Cartesian product; pointwise-sum; F-space; nonlinear approximation; heaviside neural network; satisficing regularization
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It is shown that cartesian product and pointwise-sum with a fixed compact set preserve various approximation-theoretic properties. Results for pointwise-sum are proved for F-spaces and so hold for any normed linear space, while the other results hold in general metric spaces. Applications are given to approximation of L-p-functions on the d-dimensional cube, 1 less than or equal to p < infinity, by linear combinations of half-space characteristic functions; i.e., by Heaviside perceptron networks. (C) 2004 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
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