Stability analysis of the G-algorithm and a note on its application to sparse least squares problems

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

The G-algorithm was proposed by Bareiss [1] as a method for solving the weighted linear least squares problem. It is a square root free algorithm similar to the fast Givens method except that it triangularizes a rectangular matrix a column at a time instead of one element at a time. In this paper an error analysis of the G-algorithm is presented which shows that it is as stable as any of the standard orthogonal decomposition methods for solving least squares problems. The algorithm is shown to be a competitive method for sparse least squares problems. A pivoting strategy is given for heavily weighted problems similar to that in [14] for the Householder-Golub algorithm. The strategy is prohibitively expensive, but it is not necessary for most of the least squares problems that arise in practice.

Original languageEnglish (US)
Pages (from-to)507-520
Number of pages14
JournalBIT
Volume25
Issue number3
DOIs
StatePublished - Sep 1 1985

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Least Squares Problem
Stability Analysis
Linear Least Squares
Pivoting
Orthogonal Decomposition
Weighted Least Squares
Decomposition Method
Square root
Error Analysis
Error analysis
Decomposition
Necessary
Strategy

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Graphics and Computer-Aided Design
  • Computational Mathematics
  • Applied Mathematics

Cite this

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Stability analysis of the G-algorithm and a note on its application to sparse least squares problems. / Barlow, J. L.

In: BIT, Vol. 25, No. 3, 01.09.1985, p. 507-520.

Research output: Contribution to journalArticle

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