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Mathematics of Computation

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

 

 

Methods for computing and modifying the $ LDV$ factors of a matrix


Authors: Philip E. Gill, Walter Murray and Michael A. Saunders
Journal: Math. Comp. 29 (1975), 1051-1077
MSC: Primary 65F30
DOI: https://doi.org/10.1090/S0025-5718-1975-0388754-8
MathSciNet review: 0388754
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Abstract: Methods are given for computing the LDV factorization of a matrix B and modifying the factorization when columns of B are added or deleted. The methods may be viewed as a means for updating the orthogonal (LQ) factorization of B without the use of square roots. It is also shown how these techniques lead to two numerically stable methods for updating the Cholesky factorization of a matrix following the addition or subtraction, respectively, of a matrix of rank one. The first method turns out to be one given recently by Fletcher and Powell; the second method has not appeared before.


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DOI: https://doi.org/10.1090/S0025-5718-1975-0388754-8
Article copyright: © Copyright 1975 American Mathematical Society