A Note on Downdating the Cholesky Factorization

Abstract

We analyse and compare three algorithms for “downdating” the Cholesky factorization of a positive definite matrix. Although the algorithms are closely related, their numerical properties differ. Two algorithms are stable in a certain “mixed” sense while the other is unstable. In addition to comparing the numerical properties of the algorithms, we compare their computational complexity and their suitability for implementation on parallel or vector computers.