A Block Lanczos Method for Computing the Singular Values and Corresponding Singular Vectors of a Matrix

Gene H. Golub; Franklin T. Luk; Michael L. Overton

doi:10.1145/355945.355946

A Block Lanczos Method for Computing the Singular Values and Corresponding Singular Vectors of a Matrix

Gene H. Golub, Franklin T. Luk, Michael L. Overton

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Pages (from-to)	149-169
Number of pages	21
Journal	ACM Transactions on Mathematical Software (TOMS)
Volume	7
Issue number	2
DOIs	https://doi.org/10.1145/355945.355946
State	Published - Jun 1 1981

Keywords

block Lanczos method
large sparse matrtx
singular values
singular vectors
smgular-value decomposltmn
upper triangular band matrix

ASJC Scopus subject areas

Software
Applied Mathematics

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10.1145/355945.355946

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KW - singular vectors

KW - smgular-value decomposltmn

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A Block Lanczos Method for Computing the Singular Values and Corresponding Singular Vectors of a Matrix

Abstract

Keywords

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