Robust incomplete factorization for nonsymmetric matrices

Author(s) : Amin Rafiei , Matthias Bollhöfer

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 26-2008

MSC 2000

65F10 Iterative methods for linear systems

65F50 Sparse matrices

Abstract :
In this paper a new incomplete LU factorization preconditioner for nonsymmetric matrices is being considered that is also breakdown-free (no zero pivots occurs) for positive definite matrices. The L factor is extracted as a by-product of an AINV process that only uses the information of matrix A and computes just one of the factors of the AINV process. The pivots of the AINV are also used as diagonal entries of U . Since dealing with the AINV provides left-looking and right-looking versions for this preconditioner dropping on L is performed with respect to the information of the columns of the computed factor of AINV. The computation of the upper triangular part of U is done row-wise and exploits the row-wise information of L, previously computed rows of U and the upper triangular part of A. The row-wise computation of U prepares the opportunity to use the inverse-based dropping strategies for its entries. Numerical experiments show that the left-looking version of the preconditioner is significantly faster than its right-looking version in terms of preconditioning time and both are effective as each other to reduce the number of iterations. Comparisons of the new method with AINV and ILUT methods are also presented.

Keywords : factorization, sparse matrices, schur-complement, condition estimator, inverse-based dropping, rightlooking AINV, left-looking AINV, linked list