New bounds on the zeros of spline functions
type: Item
instance of: scholarly article
title: New bounds on the zeros of spline functions
zbMATH Open document ID: 0799.41012
published in: Journal of Approximation Theory
publication date: 1994-02-17T00:00:00Z
review text: For a finite real sequence \({\mathbf a} = (a_ 0,\dots,a_ k)\) the number of strong (weak) sign changes is defined as the minimum (maximum) number of sign changes in \({\mathbf a}\) gained by assigning signs to zero entries. In Theorem 1, the author shows that, under a certain condition, the number of zeros of a spline function is bounded by the number of strong sign changes in its sequence of \(B\)-spline coefficients. By writing a general spline function as a sum of functions which satisfy the given condition, he deduces known bounds on zeros and sign changes and he can show that the number of zeros of any spline function is bounded by the number of weak sign changes in its sequence of \(B\)-spline coefficients, where the zero count is stronger than that previously used.
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 503002
zbMATH Keywords: \(B\)-spline coefficients
author: Tim N. T. Goodman
reviewed by: Jürgen Müller
MaRDI profile type: Publication
full work available at URL: jath.1994.1009
OpenAlex ID: W2042937898
DOI: 10.1006/JATH.1994.1009
description: scientific article; zbMATH DE number 503002