On the modification of factorizations
Authors:
R. Fletcher and M. J. D. Powell
Journal:
Math. Comp. 28 (1974), 10671087
MSC:
Primary 65F30
MathSciNet review:
0359297
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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:
http://dx.doi.org/10.1090/S00255718197403592971
PII:
S 00255718(1974)03592971
Keywords:
Matrix updating,
error analysis,
updating a triangular factorization,
quasiNewton method,
positive definite matrix,
rank one matrix,
rank one correction
Article copyright:
© Copyright 1974
American Mathematical Society
