Stability of parallel triangular system solvers

Higham, Nicholas J. (1995) Stability of parallel triangular system solvers. SIAM Journal on Scientific Computing, 16 (2). pp. 400-413. ISSN 1095-7197

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Abstract

Several parallel algorithms have been proposed for the solution of triangular systems. The stability of four of them is analysed here: a fan-in algorithm, a block elimination method, a method based on a factorized power series expansion of the matrix inverse, and a method based on a divide and conquer matrix inversion technique. New forward error and residual bounds are derived, including an improvement on the bounds of Sameh and Brent for the fan-in algorithm. A forward error bound is identified that holds not only for all the methods described here, but for any triangular equation solver that does not rely on algebraic cancellation; among the implications of the bound is that any such method is extremely accurate for certain special types of triangular systems.

Item Type:	Article
Uncontrolled Keywords:	triangular system, matrix inversion, parallel algorithms, fan-in operation, numerical stability, rounding error analysis
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/338

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