Experiments on error growth associated with some linear least-squares procedures

Author:
T. L. Jordan

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

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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 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 , 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 systems of linear equations. Some effects of pivoting in each of the procedures are included.

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DOI:
https://doi.org/10.1090/S0025-5718-1968-0229373-X

Article copyright:
© Copyright 1968
American Mathematical Society