Shape-preserving approximation by polynomials
type: Item
instance of: scholarly article
title: Shape-preserving approximation by polynomials
zbMATH Open document ID: 0969.41007
DOI: 10.1016/S0377-0427(00)00338-1
published in: Journal of Computational and Applied Mathematics
publication date: 2000-11-20T00:00:00Z
review text: This is a survey article on developments and achievements over the past decade, or so in the field of shape-preserving approximation by polynomials. The survey is of the works on preserving certain intrinsic `shape' properties of the approximant function on a finite interval, such as its sign in all or part of the interval, its monotonicity, convexity, etc.
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41-02
zbMATH DE Number: 1533128
author: D. Leviatan
reviewed by: Ganesh Datta Dikshit
MaRDI profile type: Publication
cites work: Convex polynomial and spline approximation in \(L_ p, 0<p<\infty\)
cites work: Q4938363
cites work: Polynomial approximation in \(L_ p (O<p<1)\)
cites work: Pointwise estimates for monotone polynomial approximation
cites work: Pointwise estimation of comonotone approximation
cites work: Copositive pointwise approximation
cites work: Piecewise monotone pointwise approximation
cites work: Uniform estimates for monotonic polynomial approximation
cites work: Interpolatory pointwise estimates for polynomial approximation
cites work: Constrained Approximation in Sobolev Spaces
cites work: Weak copositive and interwining approximation
cites work: Convex polynomial and spline approximation in \(C[-1,1]\)
cites work: The Degree of Copositive Approximation and a Computer Algorithm
cites work: Pointwise and uniform estimates for convex approximation of functions by algebraic polynomials
cites work: Uniform estimates of monotone and convex approximation of smooth functions
cites work: Coconvex polynomial approximation of twice differentiable functions
cites work: On copositive approximation by algebraic polynomials
cites work: Q4486601
cites work: Comonotone polynomial approximation in \(L_p[-1,1], 0<p\leq\infty\)
cites work: Degree of simultaneous coconvex polynomial approximation
cites work: The degree of coconvex polynomial approximation
cites work: Q5688974
cites work: Q4884016
cites work: Some positive results and counterexamples in comonotone approximation
cites work: Nearly comonotone approximation
cites work: Q4250294
cites work: Some positive results and counterexamples in comonotone approximation. II
cites work: More on comonotone polynomial approximation
cites work: Q2707262
cites work: Q5751340
cites work: APPROXIMATION OF MONOTONE FUNCTIONS BY MONOTONE POLYNOMIALS
cites work: One example in monotone approximation
cites work: Q3913213
cites work: Q4000219
cites work: A counterexample in comonotone approximation in $L^p$ space
cites work: A counterexample in copositive approximation
cites work: ON COMONOTONE APPROXIMATION BY POLYNOMIALS IN Lp SPACE
description: scientific article; zbMATH DE number 1533128