Optimal interpolation with polynomials having fixed roots
type: Item
instance of: scholarly article
title: Optimal interpolation with polynomials having fixed roots
zbMATH Open document ID: 0653.41004
DOI: 10.1016/0021-9045(87)90075-X
author: Theodore Kilgore
published in: Journal of Approximation Theory
publication date: 1987-01-01T00:00:00Z
review text: The author investigates optimal interpolation of potor transforms every continuous, n-convex function into an r-convex function. Their proof is based on the fact that the Bernstein polynomials of a continuous, n- convex function F (which converges uniformly to F) are themselves n- convex. We express the result of Bojanic and Roulier in a slightly different notation and terminology and then we take a similar approach, after obtaining various decompositions of an n-convex function, to obtain new sufficient conditions that a continuous linear operator transforms every continuous n-convex function into an r-convex function.
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 4065573
zbMATH Keywords: optimal interpolation
zbMATH Keywords: Bernstein polynomials
zbMATH Keywords: n-convex function
MaRDI profile type: Publication
cites work: Proof of the conjectures of Bernstein and Erdős concerning the optimal nodes for polynomial interpolation
cites work: Some remarks on polynomials
cites work: Optimization of the norm of the Lagrange interpolation operator
cites work: A characterization of the Lagrange interpolating projection with minimal Tchebycheff norm
cites work: Optimal interpolation with incomplete polynomials
cites work: A note on functions with interlacing roots
description: scientific article; zbMATH DE number 4065573