TY - JOUR
T1 - On graded QR decompositions of products of matrices
JF - Electronic Transactions on Numerical Analysis
Y1 - 1995
A1 - Stewart, G.W.
AB - This paper is concerned with the singular values and vectors of a product Mm =A1A2 ... Am of matrices of order n. The chief difficulty with computing them directly from Mm is that with increasing m the ratio of the small to the large singular values of Mm may fall below the rounding unit, so that the former are computed inaccurately. The solution proposed here is to compute recursively the factorization Mm = QRPT, where Q is orthogonal, R is a graded upper triangular, and PT is a permutation.
VL - 3
ER -