Generalized qd algorithm and Markov-Bernstein inequalities for Jacobi weight
type: Item
instance of: scholarly article
title: Generalized qd algorithm and Markov-Bernstein inequalities for Jacobi weight
zbMATH Open document ID: 1179.33010
author: André Draux
author: Borhane Moalla
author: Mohamed Sadik
published in: Numerical Algorithms
publication date: 2009-08-27T00:00:00Z
review text: The authors give new upper and lower bounds for the best constant \(M_n\) in the inequality \[ \|p'\|_{L^2(w)}\leq M_n\|p\|_{L^2(w)}, \] where \(\|f\|_{L^2(w)}= \int_{-1}^1 f^2(x)w(x)\,dx\), \(w(x)=(1-x)^\alpha(1+x)^\beta\). The result is obtained by generalization of the qd algorithm for positive definite symmetric band matrix.
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 26D05
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 5598824
zbMATH Keywords: qd algorithm
zbMATH Keywords: band matrices
zbMATH Keywords: recurrence relations
zbMATH Keywords: Jacobi weight
zbMATH Keywords: Markov-Bernstein inequalities
reviewed by: Alexei Lukashov
MaRDI profile type: Publication
full work available at URL: s11075-008-9241-4
OpenAlex ID: W2087830683
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DOI: 10.1007/S11075-008-9241-4
description: scientific article; zbMATH DE number 5598824