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 journalArticle

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 languageEnglish (US)
Pages (from-to)149-169
Number of pages21
JournalACM Transactions on Mathematical Software (TOMS)
Volume7
Issue number2
DOIs
StatePublished - 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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