A generalization of the variation diminishing property
type: Item
instance of: scholarly article
title: A generalization of the variation diminishing property
zbMATH Open document ID: 0837.15019
DOI: 10.1007/BF02432004
author: J. M. Carnicer
author: J. M. Peña
author: Tim N. T. Goodman
published in: Advances in Computational Mathematics
publication date: 1995-11-14T00:00:00Z
review text: Several generalizations of the ordinary variation diminishing property are derived in the sense that, given an \(m \times n\) totally positive matrix \(T\) and an \(n \times r\) matrix \(A\) satisfying some additional conditions, then the number of changes of sign in the consecutive \(r \times r\) minors of \(TA\) is bounded by the number of changes of sign in the consecutive \(r \times r\) minors of \(A\). This property is used to show shape preserving properties of curves generated by totally positive bases and, in particular, of \(B\)-spline curves.
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 803483
zbMATH Keywords: \(B\)-spline curves
zbMATH Keywords: variation diminishing property
zbMATH Keywords: totally positive matrix
zbMATH Keywords: totally positive bases
reviewed by: Costică Moroşanu
MaRDI profile type: Publication
cites work: Totally positive matrices
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full work available at URL: https://doi.org/10.1007/bf02432004
OpenAlex ID: W2086605233
description: scientific article; zbMATH DE number 803483