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 preconditioners 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.