Adaptive interpolation by scaled multiquadrics
type: Item
instance of: scholarly article
title: Adaptive interpolation by scaled multiquadrics
zbMATH Open document ID: 0999.41005
DOI: 10.1023/A:1014584220418
author: Mira Bozzini
author: Licia Lenarduzzi
author: Robert Schaback
published in: Advances in Computational Mathematics
publication date: 2002-06-09T00:00:00Z
review text: Given a univariate data sample, the authors present an adaptative method to select a subsample in such a way that shape preserving information is extracted, that is to say, that the interpolating function constructed by the subsample reproduces the signal with a good graphical accuracy. Unlike other known methods, the knot selection problem is solved beforehand. Then the interpolant is constructed via scaled multiquadrics and using B-spline techniques. In the way, a sufficient condition for existence of the scaled multiquadric interpolant is given. The authors also show numerical examples that show the applicability of the method and its advantages towards others, which are not always satisfied from a graphical point of view.
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A17
Mathematics Subject Classification ID: 41A27
Mathematics Subject Classification ID: 41A30
Mathematics Subject Classification ID: 41A40
Mathematics Subject Classification ID: 65D10
zbMATH DE Number: 1752552
zbMATH Keywords: conditionally positive definite radial basis functions
zbMATH Keywords: shape parameters
zbMATH Keywords: scaling
zbMATH Keywords: solvability
reviewed by: Daniel Cárdenas Morales
MaRDI profile type: Publication
full work available at URL: a:1014584220418
OpenAlex ID: W1483903670
description: scientific article; zbMATH DE number 1752552