Explicit solution of the polynomial least-squares approximation problem on Chebyshev extrema nodes
type: Item
instance of: scholarly article
title: Explicit solution of the polynomial least-squares approximation problem on Chebyshev extrema nodes
zbMATH Open document ID: 1123.65056
published in: Linear Algebra and its Applications
publication date: 2007-04-10T00:00:00Z
review text: The paper presents an explicit solution to the polynomial least squares approximation problem on Chebyshev extrema nodes. It is shown that the inverse of the normal matrix on the given set of nodes can be represented as the sum of two symmetric matrices: a full rank matrix which admits a Cholesky factorization, and a 2-rank matrix. Further, an efficient algorithm is developed and studied. The numerical properties of the proposed algorithm are thoroughly discussed. Several numerical experiments are carried out to confirm and illustrate that the proposed algorithm is fast and accurate.
reviewed by: Tzvetan Semerdjiev
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 65D15
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 90C20
zbMATH DE Number: 5141634
zbMATH Keywords: polynomial approximation
zbMATH Keywords: Cholesky factorization
zbMATH Keywords: combinatorial identities
zbMATH Keywords: least squares approximation
zbMATH Keywords: Chebyshev extrema nodes
zbMATH Keywords: algorithm
zbMATH Keywords: numerical experiments
author: A. Eisinberg
author: Giuseppe Fedele
describes a project that uses: Mathematica
describes a project that uses: OPQ
MaRDI profile type: Publication
full work available at URL: j.laa.2006.11.014
OpenAlex ID: W2111326439
cites work: Q4868585
cites work: Q4365424
cites work: Q5672035
cites work: Fast QR factorization of Vandermonde matrices
cites work: Rectangular Vandermonde matrices on Chebyshev nodes
cites work: Vandermonde systems on Gauss-Lobatto Chebyshev nodes
cites work: Q4820343
cites work: Q5689624
cites work: Q4275389
cites work: Q5585020
cites work: The special functions and their approximations. Vol. I, II
cites work: On the normal matrix of the polynomial LS problem over the Chebyshev points
cites work: Q4305272
DOI: 10.1016/J.LAA.2006.11.014
description: scientific article; zbMATH DE number 5141634