On the modification of 𝐿𝐷𝐿^{𝑇} factorizations

Fletcher, R.; Powell, M. J. D.

doi:10.1090/S0025-5718-1974-0359297-1

On the modification of $\textrm {LDL}^{T}$ factorizations
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by R. Fletcher and M. J. D. Powell PDF

Math. Comp. 28 (1974), 1067-1087 Request permission

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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