Parallel Computation of the Generalized Singular Value Decomposition

Abstract

The generalized singular value decomposition (GSVD) is the simultaneous reduction of any two matrices having the same number of columns to diagonal forms by premultiplying by two different orthogonal matrices and postmultiplying by the same nonsingular matrix. The recent advent of real time signal processing and other problems have given impetus to the development of the parallel computation of the GSVD [3,7]. Brent et al. [2] have developed a parallel algorithm on systolic array. However, their approach requires the use of different configurations of systolic arrays for singular value decomposition (SVD), QR decomposition and matrix-matrix multiplication. In addition to some difficulties in numerical treatment, how to avoid costly interfacing between these arrays and devise a single array that is capable of performing all these basic matrix computations is still an open problem.