Electronic Resource
Springer
Numerische Mathematik
22 (1974), S. 325-332
ISSN:
0945-3245
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract A direct error analysis is given for orthogonal factorization methods for calculating the least squares solution of an overdetermined system of linear equations. The direct method has the interesting advantage in that it permits the separation of errors occurring in the transformation and back-substitution phases of solution. This shows the partial elimination of potentially significant terms occurring in different stages of the algorithm. Presumably it is prudent to minimize the error at each stage of the algorithm, so it is significant that numerical evidence shows column pivoting can reduce the magnitude of these terms. This is offered as an explanation for the common observation that column pivoting is beneficial in least squares calculations. We also summarize the corresponding error analysis for the calculation of the minimum norm solution of an underdetermined system using orthogonal transformations.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01406971
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