Maintaining LU factors of a general sparse matrix☆

We dedicate this paper to Dr. James H. Wilkinson in recognition of his profound influence on LU factorization, and in the belief that 1−μ11−μ1 were among his favorite matrices.
https://doi.org/10.1016/0024-3795(87)90112-1Get rights and content
Under an Elsevier user license
open archive

Abstract

We describe a set of procedures for computing and updating an LU factorization of a sparse matrix A, where A may be square (possibly singular) or rectangular. The procedures include a Markowitz factorization and a Bartels-Golub update, similar to those of Reid (1976, 1982). The updates provided are addition, deletion or replacement of a row or column of A, and rank-one modification. (Previously, column replacement has been the only update available.)

Various design features of the implementation (LUSOL) are described, and computational comparisons are made with the LA05 and MA28 packages of Reid (1976) and Duff (1977).

Cited by (0)

☆

This research was supported by the U.S. Department of Energy Contract DE-AA03- 76SF00326, PA No. DE-AS03-76ER72018; National Science Foundation Grants DCR-8413211 and ECS-8312142; the office of Naval Research Contract N00014-85-K-0343; and the U.S. Army Research Office Contract DAAG29-84-K-0156.

Copyright © 1987 Published by Elsevier Inc.