### 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) |
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Pages (from-to) | 149-169 |

Number of pages | 21 |

Journal | ACM Transactions on Mathematical Software (TOMS) |

Volume | 7 |

Issue number | 2 |

DOIs | |

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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## Cite this

Golub, G. H., Luk, F. T., & Overton, M. L. (1981). A Block Lanczos Method for Computing the Singular Values and Corresponding Singular Vectors of a Matrix.

*ACM Transactions on Mathematical Software (TOMS)*,*7*(2), 149-169. https://doi.org/10.1145/355945.355946