Abstract
In the study of the numerical solution of sparse linear systems, several authors (Harary [1962A], Dulmage and Mendelsohn [1962A], Steward [1965A], Willoughby [1972A]) have considered the problem of ordering a sparse matrix so that it has a block structure which can be exploited efficiently for the solution of the system. We call this the “partitioning problem” and consider the related arithmetic and memory costs. In Section 3 we show that if the directed graph of the system is strongly connected then partitioning saves no arithmetic operations in an LU factorization but may save storage. On the other hand, if the directed graph of the system fails to be strongly connected, a reduction in both arithmetic and storage is possible. Some graph-theoretic preliminaries and useful operation counts are given in Section 2.
Partial support under contracts NSF GU35 and NSF GP-28271.
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© 1972 Plenum Press, New York
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Rose, D.J., Bunch, J.R. (1972). The Role of Partitioning in the Numerical Solution of Sparse Systems. In: Rose, D.J., Willoughby, R.A. (eds) Sparse Matrices and their Applications. The IBM Research Symposia Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-8675-3_16
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DOI: https://doi.org/10.1007/978-1-4615-8675-3_16
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4615-8677-7
Online ISBN: 978-1-4615-8675-3
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