Shape preserving interpolatory subdivision schemes for nonuniform data
type: Item
instance of: scholarly article
title: Shape preserving interpolatory subdivision schemes for nonuniform data
zbMATH Open document ID: 1003.41006
author: Frans Kuijt
author: Ruud van Damme
published in: Journal of Approximation Theory
publication date: 2002-07-04T00:00:00Z
full work available at URL: shape-preserving-interpolatory-subdivision-schemes-for-nonuniform-data(d7ad1458-6360-4d02-9acf-067860ce0b6a).html
review text: The article is devoted to the problem of shape preserving four-point subdivision schemes that are stationary and interpolate nonuniform univariate data \( \{ (x_i,f_i) \} \), where \( x_i \neq x_j \) if \( i \neq j \). Performed subdivision is made in a way to get the grid locally uniform. There is constructed suitable subdivision methods for the \(f\) -data preserving convexity. It is presented a sufficient condition for preservation of convexity. There is generated a continuously differentiable limit function from initial convex data. The schemes are restricted to those that reproduce quadratic polynomials. Derived schemes are third order accurate. The linear schemes are examined as well.
reviewed by: Josef Kofroň
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 1763601
zbMATH Keywords: shape preservation
zbMATH Keywords: subdivision
zbMATH Keywords: nonuniform data
zbMATH Keywords: convexity
zbMATH Keywords: monotonicity
zbMATH Keywords: locally uniform grid refinement
MaRDI profile type: Publication
OpenAlex ID: W2053280883
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DOI: 10.1006/JATH.2001.3628
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description: scientific article; zbMATH DE number 1763601