Institution: Stanford University, Department of Computer Science

Title: A block Lanczos method to compute the singular values and corresponding singular vectors of a matrix

Author: Golub, Gene H.

Author: Luk, Franklin T.

Author: Overton, Michael L.

Date: October 1977

Abstract: We present a block Lanczos method to compute the largest singular values and corresponding left and right singular vectors of a large sparse matrix. Our algorithm does not transform the matrix A but accesses it only through a user-supplied routine which computes AX or $A^t$X for a given matrix X. This paper also includes a thorough discussion of the various ways to compute the singular value decomposition of a banded upper triangular matrix; this problem arises as a subproblem to be solved during the block Lanczos procedure.

http://i.stanford.edu/pub/cstr/reports/cs/tr/77/635/CS-TR-77-635.pdf