Convergence order of interpolation process by Bernstein polynomials
type: Item
instance of: scholarly article
title: Convergence order of interpolation process by Bernstein polynomials
zbMATH Open document ID: 0686.41001
DOI: 10.1007/BF01953368
author: Jiaxing He
published in: Acta Mathematica Hungarica
publication date: 1989-01-01T00:00:00Z
review text: The convergence order of the interpolation process by S. N. Bernstein polynomials \(F_ n(f,x)\) with zeros of a Chebyshev polynomial of first kind of degree n is considered. We prove the following result: the convergence order is \[ \frac{1}{n}\omega (f',\frac{\sqrt{k-x^ 2}}{n}+\frac{1}{n^ 2})+\frac{\| f'\|}{n^ 2} \] when using the interpolation process \(F_ n(f,x)\) to approximate \(f(x)\in C^ 1[-1,1]\) on [-1,1].
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A36
zbMATH DE Number: 4124301
zbMATH Keywords: Bernstein polynomials
zbMATH Keywords: Chebyshev polynomial
zbMATH Keywords: convergence order
MaRDI profile type: Publication
cites work: A new proof of A. F. Timan's approximation theorem. II
cites work: On an interpolation process of S. N. Bernstein
cites work: О Некоторых Интерполяционных Процессах С. Н. Бернштейна
description: scientific article; zbMATH DE number 4124301