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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Experiments on error growth associated with some linear least-squares procedures
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by T. L. Jordan PDF
Math. Comp. 22 (1968), 579-588 Request permission

Abstract:

Some numerical experiments were performed to compare the performance of procedures for solving the linear least-squares problem based on GramSchmidt, Modified Gram-Schmidt, and Householder transformations, as well as the classical method of forming and solving the normal equations. In addition, similar comparisons were made of the first three procedures and a procedure based on Gaussian elimination for solving an $n \times n$ system of equations. The results of these experiments suggest that: (1) the Modified Gram-Schmidt procedure is best for the least-squares problem and that the procedure based on Householder transformations performed competitively; (2) all the methods for solving least-squares problems suffer the effects of the condition number of $\begin {array}{*{20}{c}} A & {^T} & A \\ \end {array}$, although in a different manner for the first three procedures than for the fourth; and (3) the procedure based on Gaussian elimination is the most economical and essentially, the most accurate for solving $n \times n$ systems of linear equations. Some effects of pivoting in each of the procedures are included.
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Additional Information
  • © Copyright 1968 American Mathematical Society
  • Journal: Math. Comp. 22 (1968), 579-588
  • MSC: Primary 65.35
  • DOI: https://doi.org/10.1090/S0025-5718-1968-0229373-X
  • MathSciNet review: 0229373