Sparsity structure and Gaussian elimination

Authors:
I. S. Duff;A. M. Erisman;C. W. Gear;J. K. Reid
Affiliations:
Boeing Computer Services, Inc., Seattle, WA;Boeing Computer Services, Inc., Seattle, WA;Univ. of Illinois, Urbana;Harwell Laboratory, Oxon, UK
Venue:
ACM SIGNUM Newsletter
Year:
1988

Citing 1
Cited 2

An Implementation of Tarjan's Algorithm for the Block Triangularization of a Matrix

ACM Transactions on Mathematical Software (TOMS)

Preconditioning techniques for large linear systems: a survey

Journal of Computational Physics
Fast methods for computing selected elements of the green's function in massively parallel nanoelectronic device simulations

Euro-Par'13 Proceedings of the 19th international conference on Parallel Processing

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we collate and discuss some results on the sparsity structure of a matrix. If a matrix is irreducible, Gaussian elimination yields an LU factorization in which L has at least one entry beneath the diagonal in every column except the last and U has at least one entry to the right of the diagonal in every row except the last. If this factorization is used to solve the equation Ax=b, the intermediate vector has an entry in its last component and the solution x is full. Furthermore, the inverse of A is full.Where the matrix is reducible, these results are applicable to the diagonal blocks of its block triangular form.