Report Number: CS-TR-77-635
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
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.