On the modification of 𝐿𝐷𝐿^{𝑇} factorizations

Abstract

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.