Computing the Generalized Singular Value Decomposition

Publisher Website
Google Scholar
Abstract
We present a new numerical method for computing the GSVD [36, 27] of two matrices A and B. This method is a variation on Paige''s method [30]. It differs from previous algorithms in guaranteeing both backward stability and con- vergence. There are two innovations. The first is a new pre- processing step which reduces A and B to upper triangular forms satisfying certain rank conditions. The second is a new 2 by 2 triangular GSVD algorithm, which constitutes the inner loop of Paige''s method. We present proofs of stability and convergence of our method, and demonstrate examples on which all previous algorithms fail.

This publication has 26 references indexed in Scilit: