Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43520171031Complete pivoting strategy for the $IUL$ preconditioner obtained from Backward Factored APproximate INVerse process141714561033ENA.RafieiDepartment of Applied Mathematics, Hakim Sabzevari University, Sabzevar, Iran.M.BollhoeferInstitute computational Mathematics, Technische Universitat Braunschweig, D-38106 Braunschweig, Germany.Journal Article20160102In 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 $\alpha$ to control the complete pivoting process. We have studied the effect of different values of $\alpha$ 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 the Reverse Cuthill-Mckee (RCM) and multilevel nested dissection reordering.http://bims.iranjournals.ir/article_1033_a0a902a62988d3118f5b4b4d8b35504d.pdf