Tensor-product monotonicity preservation
type: Item
instance of: scholarly article
title: Tensor-product monotonicity preservation
zbMATH Open document ID: 0914.65007
DOI: 10.1023/A:1018906027191
author: Michael S. Floater
author: J. M. Peña
published in: Advances in Computational Mathematics
publication date: 1999-03-11T00:00:00Z
review text: The authors study conditions concerning monotonicity of bivariate functions defined as tensor products. Monotonicity-preserving spline schemes are important in the context of the approximation and interpolation (of tensor product data) when it is known that the discrete data originate from an originally monotonically increasing function. Bernstein-Bézier and \(B\)-spline methods involve the use of a so-called ``control net'', given by the set of Bernstein-Bézier/\(B\)-spline control points, and it is highly desirable to know conditions for the control net such that the implied analytical function is monotonic. The authors study and derive conditions for control nets relating monotonic behavior of the nets to the resulting functions. In particular, conditions are provided for general-monotonicity preservation, i.e., for preservative of monotonicity in arbitrary directions, not just axial directions.
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 1234315
zbMATH Keywords: monotonicity preservation
zbMATH Keywords: bivariate tensor products
zbMATH Keywords: Bernstein-Bézier methods
zbMATH Keywords: control net
zbMATH Keywords: \(B\)-spline methods
zbMATH Keywords: spline schemes
reviewed by: Bernd Hamann
MaRDI profile type: Publication
full work available at URL: a:1018906027191
OpenAlex ID: W159286662
description: scientific article; zbMATH DE number 1234315