Methods for computing and modifying the 𝐿𝐷𝑉 factors of a matrix

Abstract

Methods are given for computing the <italic>LDV</italic> factorization of a matrix <italic>B</italic> and modifying the factorization when columns of <italic>B</italic> are added or deleted. The methods may be viewed as a means for updating the orthogonal (<italic>LQ</italic>) factorization of <italic>B</italic> without the use of square roots. It is also shown how these techniques lead to two numerically stable methods for updating the Cholesky factorization of a matrix following the addition or subtraction, respectively, of a matrix of rank one. The first method turns out to be one given recently by Fletcher and Powell; the second method has not appeared before.