On the normal matrix of the polynomial LS problem over the Chebyshev points
type: Item
instance of: scholarly article
title: On the normal matrix of the polynomial LS problem over the Chebyshev points
zbMATH Open document ID: 1049.65028
author: Paolo Pugliese
published in: Linear Algebra and its Applications
publication date: 2004-08-06T00:00:00Z
review text: Let \(V = [x_i^{j-1}]\) be an \(n\times m\) (\(n\geq m\)) Vandermonde matrix with the Chebyshev nodes \(x_i = \cos(\pi (2i-1) /2n)\). This paper provides an explicit formula for the Cholesky factor of the matrix \(V^T V\), leading to an \(O(m (m+n) )\) method for solving polynomial approximation problems. It turns out that the entries of the Cholesky factor and its inverse can be represented as integers divided by powers of two. Numerical experiments suggest that this approach is more efficient but also sometimes less accurate than methods based on orthogonal polynomials for solving approximation problems.
reviewed by: Daniel Kressner
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 26C05
Mathematics Subject Classification ID: 65F05
zbMATH DE Number: 2081746
zbMATH Keywords: polynomial approximation
zbMATH Keywords: Vandermonde matrix
zbMATH Keywords: Cholesky factorization
zbMATH Keywords: least squares method
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
full work available at URL: j.laa.2003.09.002
OpenAlex ID: W2005196902
cites work: Optimal sampling schedule for parameter estimation of linear models with unknown but bounded measurement errors
cites work: Q4868585
cites work: Q5672035
cites work: Fast QR factorization of Vandermonde matrices
cites work: Rectangular Vandermonde matrices on Chebyshev nodes
cites work: Vandermonde matrices on integer nodes: The rectangular case
cites work: Q5533821
cites work: Q3359644
cites work: Q4320535
cites work: Q4275389
DOI: 10.1016/J.LAA.2003.09.002
description: scientific article; zbMATH DE number 2081746