A Block Lanczos Method for Computing the Singular Values and Corresponding Singular Vectors of a Matrix
Gene Howard Golub, Franklin T. Luk, Michael L. Overton · ACM Transactions on Mathematical Software · 1981
We present a block Lanczos method for computing the greatest singular values and associated vectors of a large and sparse matrix, say A. Our algorithm does not transform A but accesses it through a user-supplied routine that computes the product AX or A tX for a given matrix X.This paper includes a discussion of the various ways to compute the singular-value decomposition of an upper triangular band matrix, this problem arises as a subproblem to be solved in the block Lanczos procedure.