Volume 36, pp. 39-53, 2009-2010.

$P$-regular splitting iterative methods for non-Hermitian positive definite linear systems

Cheng-Yi Zhang and Michele Benzi

Abstract

We study the convergence of $P$-regular splitting iterative methods for non-Hermitian positive definite linear systems. Our main result is that $P$-regular splittings of the form $A=M-N$, where $N=N^{\ast }$, are convergent. Natural examples of splittings satisfying the convergence conditions are constructed, and numerical experiments are performed to illustrate the convergence results obtained.

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Key words

Non-Hermitian positive definite matrices, $P$-regular splitting, convergence, SOR methods, preconditioned GMRES

AMS subject classifications

65F10, 15A15, 15F10.