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A number of methods are compared for modifying an      L D L T 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.

On the modification of 𝐿𝐷𝐿^{𝑇} factorizations