The Effects of Rounding Error on an Algorithm for Downdating a Cholesky Factorization

Let the positive definite matrix A have a Cholesky factorizationA= R^TR. For a given vector xsuppose that ? =A - xx^T has a Choleskyfactorization ? = ^T.This paper considers an algorithm for computing from R and x and an extension for removing a row from the QR factorizationof a regression problem. It is shown that the algorithm is stablein the presence of rounding errors. However, it is also shownthat the matrix can be a very ill-conditioned function of R and x.