New breakdown-free variant of AINV method for nonsymmetric positive definite matrices

Authors:
A. Rafiei;F. Toutounian
Affiliations:
Department of Mathematics, Ferdowsi University of Mashhad, P.O. Box 91775-1159, Mashhad, Iran;Department of Mathematics, Ferdowsi University of Mashhad, P.O. Box 91775-1159, Mashhad, Iran
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 5
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Breakdown-free version of ILU factorization for nonsymmetric positive definite matrices

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Abstract

This paper proposes a new breakdown-free preconditioning technique, called SAINV-NS, of the AINV method of Benzi and Tuma for nonsymmetric positive definite matrices. The resulting preconditioner which is an incomplete factorization of the inverse of a nonsymmetric matrix will be used as an explicit right preconditioner for QMR, BiCGSTAB and GMRES(m) methods. The preconditoner is reliable (pivot breakdown can not occur) and effective at reducing the number of iterations. Some numerical experiments on test matrices are presented to show the efficiency of the new method and comparing to the AINV-A algorithm.