Two problems on interpolation
type: Item
instance of: scholarly article
title: Two problems on interpolation
zbMATH Open document ID: 0848.41003
DOI: 10.1007/BF01208434
author: Eli Levin
author: Boris Shekhtman
published in: Constructive Approximation
publication date: 1996-03-17T00:00:00Z
review text: The authors pose two open problems concerning polynomial interpolation, provide some information on related known results, and give conjectures for the answers. The two problems are the following, where \(\Delta_n\) is a set of \(n\) distinct interpolation points in the interval \([0, 1]\). Firstly, given a complex-valued continuous function on \([0, 1]\), it is possible to find sets \(\Delta_n\), such that the resulting interpolation polynomials of degree \(n\) converge uniformly to the given function. Secondly, is a Newton type interpolation procedure always possible, i.e. given a real-valued continuous function on \([0, 1]\), are there point sets with \(\Delta_n \subset \delta_{n+1}\), such that the corresponding interpolation polynomials converge uniformly to the function.
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A10
zbMATH DE Number: 856602
reviewed by: E. Quak
MaRDI profile type: Publication
cites work: Interpolation of individual functions
cites work: Q4486614
description: scientific article; zbMATH DE number 856602