Approximative Compactness of Linear Combinations of Characteristic Functions

Autoři: RNDr. Věra Kůrková, DSc.
Rok vydání: 2020
Typ publikace: Článek v odborném periodiku
Periodikum: Journal of Approximation Theory
Projekty: Schopnosti a omezení mělkých a hlubokých sítí
Bibliografická citace: 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
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Abstrakt

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.