Preconditioners for least squares problems by LU factorization
type: Item
instance of: scholarly article
title: Preconditioners for least squares problems by LU factorization
zbMATH Open document ID: 0924.65034
author: K. Appert
publication date: 1999-06-21T00:00:00Z
full work available at URL: https://eudml.org/doc/119995
full work available at URL: pp26-35.html
review text: The authors consider the problem of finding suitable preconditioners in the iterative solution of least squares problems \(\min\| Ax-b\|_2\) where the rectangular matrix \(A\) is large and sparse. Two basic conjugate gradient methods using an appropriate submatrix \(A_1\) as a preconditioner are proposed and bounds for the rate of convergence are derived. It is shown how one of these methods can be adapted to solve a generalized least squares problem. An algorithm for selecting \(n\) linearly independent rows from \(A\) to form \(A_1\) is outlined. The methods are tested on some sparse rectangular matrices from the Harwell-Boeing sparse matrix collection. It follows from the comparison results that the preconditioned conjugate method is much better than the conjugate gradient method.
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 1306002
zbMATH Keywords: linear least squares
zbMATH Keywords: conjugate gradient method
zbMATH Keywords: preconditioners
zbMATH Keywords: convergence
zbMATH Keywords: algorithm
zbMATH Keywords: sparse rectangular matrices
reviewed by: Petko Hr. Petkov
MaRDI profile type: Publication
published in: ETNA - Electronic Transactions on Numerical Analysis
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description: scientific article; zbMATH DE number 1306002