Complete pivoting strategy for the IUL preconditioner obtained from Backward Factored APproximate INVerse process

In this paper, we use a complete pivoting strategy to compute the IUL preconditioner obtained as the by-product of the Backward Factored APproximate INVerse process. This pivoting is based on the complete pivoting strategy of the Backward IJK version of Gaussian Elimination process. There is a parameter to control the complete pivoting process. We have studied the effect of different values of on the quality of the IUL preconditioner. For the numerical experiments section, the IUL factorization which is coupled with the complete pivoting is compared to the ILUTP and to the left-looking version of RIF which is coupled with the complete pivoting strategy. As the preprocessing, we have applied the maximum weighted matching coupled with the Reverse Cuthill-Mckee (RCM) and multilevel nested dissection reordering.