COMPUTING THE GENERALIZED SINGULAR-VALUES VECTORS OF LARGE SPARSE OR STRUCTURED MATRIX PAIRS

We present a numerical algorithm for computing a few extreme generaliz ed singular values and corresponding vectors of a sparse or structured matrix pair {A,B}. The algorithm is based on the CS decomposition and the Lanczos bidiagonalization process. At each iteration step of the Lanczos process, the solution to a linear least squares problem with ( A(T),B-T)(T) as the coefficient matrix is approximately computed, and this consists the only interface of the algorithm with the matrix pair {A,B}. Numerical results are also given to demonstrate the feasibilit y and efficiency of the algorithm.