A variation of Paige’s algorithm is presented for computing the generalized singular value decomposition (GSVD) of two matrices A and B. 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 × 2 triangular GSVD algorithm, which constitutes the inner loop of Paige’s algorithm. Proofs of stability and high accuracy of the 2 × 2 GSVD algorithm are presented and are demonstrated using examples on which all previous algorithms fail.
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Bai et al. (1993) studied this question.
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