COMPUTING THE GENERALIZED SINGULAR-VALUE DECOMPOSITION

A variation of Paige's algorithm is presented for computing the genera lized singular value decomposition (GSVD) of two matrices A and B. The re are two innovations. The first is a new preprocessing step which re duces A and B to upper triangular forms satisfying certain rank condit ions. The second is a new 2 x 2 triangular GSVD algorithm, which const itutes the inner loop of Paige's algorithm. Proofs of stability and hi gh accuracy of the 2 x 2 GSVD algorithm are presented and are demonstr ated using examples on which all previous algorithms fail.