An ILU preconditioner for nonsymmetric positive definite matrices by using the conjugate Gram-Schmidt process

Authors:
Mansoor Rezghi;S. Mohammad Hosseini
Affiliations:
Department of Mathematics, Tarbiat Modarres University, Tehran, Iran;Department of Mathematics, Tarbiat Modarres University, Tehran, Iran
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

Citing 5
Cited 1

A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method

SIAM Journal on Scientific Computing
A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems

SIAM Journal on Scientific Computing
Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method

SIAM Journal on Scientific Computing
Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems

SIAM Journal on Matrix Analysis and Applications
Preconditioning techniques for large linear systems: a survey

Journal of Computational Physics

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

Journal of Computational and Applied Mathematics

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Abstract

The present paper investigates the approach mentioned, but not developed, in [Benzi, Tuma, Numer. Linear Algebra Appl. 10 (2003)]. In this approach, using a conjugate Gram-Schmidt algorithm, an ILU preconditioner whose existence is guaranteed for any nonsingular (symmetric and nonsymmetric) real positive definite matrix is obtained. Numerical results on some nonsymmetric positive definite matrices demonstrate the efficiency of the method.