\(GB\)-splines of arbitrary order
type: Item
instance of: scholarly article
title: \(GB\)-splines of arbitrary order
zbMATH Open document ID: 0952.65017
DOI: 10.1016/S0377-0427(98)00265-9
author: Boris Kvasov
author: Pairote Sattayatham
published in: Journal of Computational and Applied Mathematics
publication date: 2001-01-02T00:00:00Z
review text: The authors expand the main results of \textit{B. I. Kvasov} [Ann. Numer. Math. 3, No. 1-4, 139-149 (1996; Zbl 0873.65006)] to generalized \(B\)-splines (\(GB\)-splines) of arbitrary order. These \(GB\)-splines are nonnegative functions with supports of minimal length which form a partition of unity. Explicit formulae and recurrence relations for the calculation of \(GB\)-splines are given. The main properties of \(GB\)-splines and their series, such as partition of unity, shape-preserving properties, invariance with respect to affine transformations are derived. It is shown that the \(GB\)-spline series is a variation diminishing function and the systems of \(GB\)-splines are weak Chebyshevian systems.
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 1367884
zbMATH Keywords: spline
zbMATH Keywords: generalized \(B\)-spline (\(GB\)-spline)
zbMATH Keywords: weak Chebyshevian system
zbMATH Keywords: variation diminishing
zbMATH Keywords: shape-preserving approximation
reviewed by: Margit Lenard
MaRDI profile type: Publication
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Wikidata QID: Q126804679
full work available at URL: s0377-0427(98)00265-9
OpenAlex ID: W2136738312
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description: scientific article; zbMATH DE number 1367884