Constructive methods in convex \(C^ 2\) interpolation using quartic splines
type: Item
instance of: scholarly article
title: Constructive methods in convex \(C^ 2\) interpolation using quartic splines
zbMATH Open document ID: 0858.65009
DOI: 10.1007/BF02141744
author: Bernd Mulansky
author: Jochen W. Schmidt
published in: Numerical Algorithms
publication date: 1997-03-11T00:00:00Z
review text: This paper is concerned with a method for convexity preserving \(C^2\) interpolation which uses quartic splines on refined grids and is successful for all strictly convex data sets. The original grid is refined with one additional knot in each subinterval. These added knots are chosen in order to retain the desired convexity. The authors propose several explicit algorithms and two methods for the placement of the knots. Since the interpolants are not uniquely determined, a positive definite quadratic optimization problem has to be solved. Some results of numerical experiments are reported and discussed.
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 915386
zbMATH Keywords: convexity preserving interpolation
zbMATH Keywords: quartic splines
zbMATH Keywords: strictly convex data sets
zbMATH Keywords: algorithms
zbMATH Keywords: numerical experiments
reviewed by: Luigi Gatteschi
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02141744
OpenAlex ID: W2027282094
description: scientific article; zbMATH DE number 915386