Approximative Compactness of Linear Combinations of Characteristic Functions

Authors: P.C. Kainen, Věra Kůrková, A. Vogt
Publication year: 2020
Publication type: Článek v odborném periodiku
Periodical: Journal of Approximation Theory
Projects: Capabilities and limitations of shallow and deep networks
Bibliographic citation: KAINEN, P.C., KŮRKOVÁ, Věra, VOGT, A. Approximative Compactness of Linear Combinations of Characteristic Functions. Journal of Approximation Theory. 2020, 257(September 2020), 105435. ISSN 0021-9045. E-ISSN 1096-0430
Dostupné z: doi:10.1016/j.jat.2020.105435.
DOI: 10.1016/j.jat.2020.105435
ID: 524108
Online record: View online record

Abstract

Best approximation by the set of all n-fold linear combinations of a family of characteristic functions of measurable subsets is investigated. Such combinations generalize Heaviside-type neural networks. Existence of best approximation is studied in terms of approximative compactness, which requires convergence of distance-minimizing sequences.