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 dier.,Two algorithms are stable in a certain “mixed” sense, while the other is unstable. In ad- dition to comparing the numerical properties of the algorithms, we compare their computational complexity and their suitability for implementation on parallel or vector computers. Comments