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Mathematics of Computation

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On the modification of $ {\rm LDL}\sp{T}$ factorizations

Authors: R. Fletcher and M. J. D. Powell
Journal: Math. Comp. 28 (1974), 1067-1087
MSC: Primary 65F30
MathSciNet review: 0359297
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Abstract: A number of methods are compared for modifying an $ LD{L^T}$ 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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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

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