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Accuracy of Gram–Schmidt orthogonalization and Householder transformation for the solution of linear least squares problems

✍ Scribed by James W. Longley; Roger D. Longley

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
56 KB
Volume
4
Category
Article
ISSN
1070-5325

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✦ Synopsis

Accuracy of a Gram-Schmidt algorithm for the solution of linear least squares equations is compared with accuracy of least squares subroutines in three highly respected mathematical packages that use Householder transformations. Results from the four programs for 13 test problems were evaluated at 16 digit precision on four different desktop computers using four different compilers. Singular values obtained from the different programs are compared and the effect of pivoting to improve the accuracy is discussed. Solution vectors from the program using the Gram-Schmidt algorithm were generally more accurate or comparable to solution vectors from the programs using the Householder transformations.

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