A perturbation analysis of the problem of downdating a Cholesky factorization

AbstractThe rank-one modification of a Cholesky factorization R>TR−zzT=DTD, where R and D are upper triangular matrices and z is a column vector, is called the downdating problem. There are many articles devoted to this problem, due to its broad range of applications and numerical difficulty. This paper serves as a first-order parametrized perturbation analysis of this problem