Computing the Generalized Singular Value Decomposition

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.

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