On the modification of factorizations

Authors:
R. Fletcher and M. J. D. Powell

Journal:
Math. Comp. **28** (1974), 1067-1087

MSC:
Primary 65F30

DOI:
https://doi.org/10.1090/S0025-5718-1974-0359297-1

MathSciNet review:
0359297

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Abstract | References | Similar Articles | Additional Information

Abstract: A number of methods are compared for modifying an factorization of a positive definite matrix *A* when a matrix of rank one is added to *A*. Both the efficiency and error propagation characteristics are discussed, and it is shown that a suitable method must be chosen with care. An error analysis of some of the algorithms is given which has novel features. A worked example which also illustrates error growth is presented. Extensions to the methods are desribed which enable them to be used advantageously in representing and updating positive semidefinite matrices.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1974-0359297-1

Keywords:
Matrix updating,
error analysis,
updating a triangular factorization,
quasi-Newton method,
positive definite matrix,
rank one matrix,
rank one correction

Article copyright:
© Copyright 1974
American Mathematical Society