An Algorithm for the Generalized Singular Value Decomposition on Massively Parallel Computers

A new algorithm for computing the generalized singular value decomposition that diagonalizes two matrices is introduced. First, two existing algorithms are studied, one due to Paige and the other to Han and Veselic. The former requires only orthogonal plane transformations, resulting in two matrices with parallel rows. The latter employs nonsingular (not necessarily orthogonal) transformations to directly diagonalize the two data matrices. For many applications, it is preferable to be given both the diagonal matrices and the transformation matrices explicitly. Our algorithm has the advantages that the nonsingular transformation is readily available, computation of transformations is simple, and the convergence test is efficient in a parallel computing environment. We present implementation results, obtained on a Connection Machine 2, to compare our new algorithm with that of Paige.