A Comparison of Some Methods for Solving Sparse Linear Least-Squares Problems

The method of normal equations, the Peters-Wilkinson algorithm and an algorithm based on Givens rotations for solving large sparse linear least squares problems are discussed and compared. Numerical experiments show that the method of normal equations should be considered when the observation matrix...

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Bibliographic Details
Published inSIAM journal on scientific and statistical computing Vol. 4; no. 2; pp. 177 - 187
Main Authors George, Alan, Heath, Michael T., Ng, Esmond
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.06.1983
Subjects
Algorithms
Decomposition
Experiments
Linear equations
Sparsity
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Summary:The method of normal equations, the Peters-Wilkinson algorithm and an algorithm based on Givens rotations for solving large sparse linear least squares problems are discussed and compared. Numerical experiments show that the method of normal equations should be considered when the observation matrix is sparse and well conditioned. For ill-conditioned problems, the algorithm based on Givens rotations is preferable.
ISSN:0196-5204
1064-8275
2168-3417
1095-7197
DOI:10.1137/0904013