Stability of the partitioned inverse method for parallel solution of sparse triangular systems

Higham, Nicholas J. and Pothen, Alex (1994) Stability of the partitioned inverse method for parallel solution of sparse triangular systems. SIAM Journal on Scientific Computing, 15 (1). pp. 139-148. ISSN 1095-7197

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Abstract

Several authors have recently considered a parallel method for solving sparse triangular systems with many right-hand sides. The method employs a partition into sparse factors of the product form of the inverse of the coefficient matrix. It is shown here that while the method can be unstable, stability is guaranteed if a certain scalar that depends on the matrix and the partition is small and that this scalar is small when the matrix is well conditioned. Moreover, when the partition is chosen so that the factors have the same sparsity structure as the coefficient matrix, the backward error matrix can be taken to be sparse.

Item Type:	Article
Uncontrolled Keywords:	sparse matrix, triangular system, substitution algorithm, parallel algorithm, rounding error analysis, matrix inverse
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User:	Ms Lucy van Russelt
Date Deposited:	30 Jun 2006
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/341

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