Admissible slopes for monotone and convex interpolation
type: Item
instance of: scholarly article
title: Admissible slopes for monotone and convex interpolation
zbMATH Open document ID: 0624.41001
DOI: 10.1007/BF01397546
author: Alan Edelman
author: Charles A. Micchelli
published in: Numerische Mathematik
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133205
review text: In many applications, interpolation of experimental data exhibiting some geometric property such as nonnegativity, monotonicity or convexity is unacceptable unless the interpolant reflects these characteristics. This paper identifies admissible slopes at data points of various \(C^ 1\) interpolants which ensure a desirable shape. We dicuss this question, in turn for the following function classes commonly used for shape preserving interpolations: monotone polynomials, \(C^ 1\) monotone piecewise polynomials, convex polynomials, parametric cubic curves and rational functions.
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A20
zbMATH DE Number: 4013207
zbMATH Keywords: shape preserving interpolations
zbMATH Keywords: monotone polynomials
zbMATH Keywords: \(C^ 1\) monotone piecewise polynomials
zbMATH Keywords: convex polynomials
zbMATH Keywords: parametric cubic curves
describes a project that uses: pchip
MaRDI profile type: Publication
cites work: Monotone Piecewise Cubic Interpolation
cites work: Piecewise Rational Quadratic Interpolation to Monotonic Data
cites work: Accurate Monotonicity Preserving Cubic Interpolation
cites work: Q5534404
cites work: On Shape Preserving Quadratic Spline Interpolation
OpenAlex ID: W2031925089
description: scientific article; zbMATH DE number 4013207