Approximative Compactness of Linear Combinations of Characteristic Functions

0524108 - ÚI 2021 RIV US eng J - Journal Article
Kainen, P.C. - Kůrková, Věra - Vogt, A.
Approximative Compactness of Linear Combinations of Characteristic Functions.
Journal of Approximation Theory. Roč. 257, September 2020 (2020), č. článku 105435. ISSN 0021-9045. E-ISSN 1096-0430
R&D Projects: GA ČR(CZ) GA18-23827S
Institutional support: RVO:67985807
Keywords : Approximative compactness * Compact sets of characteristic (indicator) functions * Symmetric difference metric * Hausdorff metric * Haar measure * Neural networks
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Impact factor: 1.091, year: 2020
Method of publishing: Limited access
http://dx.doi.org/10.1016/j.jat.2020.105435

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.
Permanent Link: http://hdl.handle.net/11104/0308450