The dual basis functions for the Bernstein polynomials
type: Item
instance of: scholarly article
title: The dual basis functions for the Bernstein polynomials
zbMATH Open document ID: 0913.41004
DOI: 10.1023/A:1018912801267
author: Bert Jüttler
published in: Advances in Computational Mathematics
publication date: 1999-05-31T00:00:00Z
review text: The Bernstein polynomials \(B^n_i\), \(i=0,1,\dots,n\) form a basis of the \((n+1)\)-dimensional real linear space \(P^n\) of all polynomials of maximal degree \(n\). The dual basis functions \(D^n_j\) with respect to the inner product of \(L^2[0,1]\) can be represented as linear combinations of the \(B^n_i\). The paper under review gives an explicit representation of the coefficients of these linear combinations in terms of products of binomial coefficients.
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 65D17
zbMATH DE Number: 1187657
zbMATH Keywords: Bernstein polynomials
zbMATH Keywords: dual basis
reviewed by: Rudolf Wegmann
MaRDI profile type: Publication
full work available at URL: a:1018912801267
OpenAlex ID: W1793687058
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description: scientific article; zbMATH DE number 1187657