Methods for computing and modifying the 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