ILU and IUL factorizations obtained from forward and backward factored approximate inverse algorithms

In this paper‎, ‎an efficient dropping criterion has been used to compute the IUL factorization obtained from Backward Factored APproximate INVerse (BFAPINV) and ILU factorization obtained from Forward Factored APproximate INVerse (FFAPINV) algorithms‎. ‎We use different drop tolerance parameters to compute the preconditioners‎. ‎To study the effect of such a dropping on the quality of the ILU and IUL factorizations‎, ‎we have used the preconditioners as the right preconditioner < s > for several linear systems and then‎, ‎the Krylov subspace methods have been used to solve the preconditioned systems‎. ‎To avoid storing matrix $A$ in two CSR and CSC formats‎, ‎the linked lists trick has been used in the implementations‎. ‎As the preprocessing‎, ‎the multilevel nested dissection reordering has also been used‎.