On the interpolation constants of Whitney
type: Item
instance of: scholarly article
title: On the interpolation constants of Whitney
zbMATH Open document ID: 0874.41006
DOI: 10.1007/BF02308550
author: N. V. Kryakin
author: M. D. Takev
published in: Mathematical Notes
publication date: 1997-07-14T00:00:00Z
review text: The main result is as follows. Theorem. Let \(f\in C[0,1]\) and \(P\) be an algebraic polynomial of degree \(\leq n-1\) such that \[ f\left ({i\over n-1} \right)= P\left({i \over n-1} \right), \quad i=0,1, \dots, n-1. \] Then \[ \sup_{0\leq x\leq 1} \bigl|f(x)-P(x) \bigr|<5 \sup_{x, x+ nh \in[0,1]} \bigl|\Delta^n_hf(x) \bigr|. \] Here \[ \Delta^n_h f(x): =\sum^n_{j =0} (-1)^j {n\choose j} f(x+jh). \]
Mathematics Subject Classification ID: 41A17
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 1028531
zbMATH Keywords: interpolation
zbMATH Keywords: Whitney's constant
reviewed by: Yuri A. Brudnyi
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1028531