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Computing the Generalized Singular Value Decomposition

Authors:
Bai, Zhaojun
Demmel, James W.
Technical Report Identifier: CSD-91-645
August 1991
CSD-91-645.pdf

Abstract: We present a new numerical method for computing the GSVD of two matrices A and B. This method is a variation on Paige's method. It differs from previous algorithms in guaranteeing both backward stability and convergence. There are two innovations. The first is a new preprocessing 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.