The block Lanczos method for linear systems with multiple right-hand sides Original Research Article

In the present paper, we present the block Lanczos method for solving linear systems with multiple right-hand sides. We define the method by using matrix-valued orthogonal polynomials and the Schur complement. As for the one right-hand side Lanczos method, the use of matrix-valued orthogonal polynomials will allow us to derive new block Lanczos-type methods such as block Lanczos/Orthodir and block BIODIR algorithms.