Conference paper
Authors list: Berdysheva, Elena E.; Dyn, Nira; Farkhi, Elza; Mokhov, Alona
Publication year: 2019
Pages: 251-264
Journal: Journal of Computational and Applied Mathematics
Volume number: 349
ISSN: 0377-0427
eISSN: 1879-1778
Open access status: Bronze
DOI Link: https://doi.org/10.1016/j.cam.2018.09.039
Conference: 2nd Conference on Subdivision, Geometric and Algebraic Methods, Isogeometric Analysis and Refinability in Italy (SMART)
Publisher: Elsevier
Abstract:
In this paper we approximate univariate set-valued functions (SVFs) of bounded variation with range consisting of general (not necessarily convex) compact sets. The approximation operators adapted to SVFs are local operators such as the symmetric Schoenberg spline operator, the Bernstein polynomial operator and the Steklov function. All operators are adapted by using metric linear combinations. Error bounds, obtained in the averaged Hausdorff metric, provide rates of approximation similar to those for real-valued functions of bounded variation. (C) 2018 Elsevier B.V. All rights reserved.
Citation Styles
Harvard Citation style: Berdysheva, E., Dyn, N., Farkhi, E. and Mokhov, A. (2019) Metric approximation of set-valued functions of bounded variation, Journal of Computational and Applied Mathematics, 349, pp. 251-264. https://doi.org/10.1016/j.cam.2018.09.039
APA Citation style: Berdysheva, E., Dyn, N., Farkhi, E., & Mokhov, A. (2019). Metric approximation of set-valued functions of bounded variation. Journal of Computational and Applied Mathematics. 349, 251-264. https://doi.org/10.1016/j.cam.2018.09.039
Keywords
SDG Areas