ISSN:
1572-9125
Keywords:
QR decomposition downdating
;
Gram-Schmidt downdating algorithm
;
Householder transformation
;
least squares problems
;
modified Gram-Schmidt algorithm
;
reorthogonalization
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract A new algorithm for downdating a QR decomposition is presented. We show that, when the columns in the Q factor from the Modified Gram-Schmidt QR decomposition of a matrixX are exactly orthonormal, the Gram-Schmidt downdating algorithm for the QR decomposition ofX is equivalent to downdating the full Householder QR decomposition of the matrixX augmented by ann ×n zero matrix on top. Using this relation, we derive an algorithm that improves the Gram-Schmidt downdating algorithm when the columns in the Q factor are not orthonormal. Numerical test results show that the new algorithm produces far more accurate results than the Gram-Schmidt downdating algorithm for certain ill-conditioned problems.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01740553
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