### 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 language | English (US) |
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Pages (from-to) | 507-520 |

Number of pages | 14 |

Journal | BIT |

Volume | 25 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1 1985 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

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*BIT*, vol. 25, no. 3, pp. 507-520. https://doi.org/10.1007/BF01935371

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Stability analysis of the G-algorithm and a note on its application to sparse least squares problems

AU - Barlow, J. L.

PY - 1985/9/1

Y1 - 1985/9/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0021973363&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0021973363&partnerID=8YFLogxK

U2 - 10.1007/BF01935371

DO - 10.1007/BF01935371

M3 - Article

AN - SCOPUS:0021973363

VL - 25

SP - 507

EP - 520

JO - BIT Numerical Mathematics

JF - BIT Numerical Mathematics

SN - 0006-3835

IS - 3

ER -