Computing the generalized singular values/vectors of large sparse or structured matrix pairs
The author derives an algorithm for computing a few extreme generalized singular values and the corresponding vectors of a sparse or structural 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 in the only interface of the algorithm with the matrix pair \(\{A,B\}\). Some numerical results are also given to demonstrate the feasibility and efficiency of the algorithm.
scientific article; zbMATH DE number 932049