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Abstract In this paper, we present a block format of left-looking AINV preconditioner for a nonsymmetric matrix. This preconditioner has block 1 × 1 or 2 × 2 pivot entries. It is introduced based on a block format of Gaussian Elimination process which has been studied in [14]. We have applied the multilevel nested dissection reordering as the preprocessing and have compared this block preconditioner by the plain left-looking AINV preconditioner. If we mix the multilevel nested dissection by the maximum weighted matching process, then the numerical experiments indicate that the number of 2 × 2 pivot entries in the block preconditioner will grow up. In this case, the block preconditioner makes GMRES method convergent in a smaller number of iterations. In the numerical section, we have also compared the ILUT and block left-looking AINV preconditioners. [ABSTRACT FROM AUTHOR]

A technique for computing an ILU preconditioner based on the factored approximate inverse (FAPINV) algorithm is presented. We show that this algorithm is well-defined for H-matrices. Moreover, when used in conjunction with Krylov-subspace-based iterative solvers such as the GMRES algorithm, results in reliable solvers. Numerical experiments on some test matrices are given to show the efficiency of the new ILU preconditioner. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we have used a complete pivoting strategy to compute the left-looking version of preconditioner. This pivoting is based on the complete pivoting strategy of the version of Gaussian Elimination process. There is a parameter to control the pivoting process. To study the effect of on the quality of the left-looking version of preconditioner with complete pivoting strategy, we have used ten different values of this parameter. In the numerical experiments section, the quality of the left-looking version of preconditioner with complete pivoting strategy has been compared to the quality of the right-looking version of this preconditioner. [Copyright &y& Elsevier]