On the Relations between ILUs and Factored Approximate Inverses

ILUs and Factorized Approximate Inverses are Strongly Related. Part I: Overview of Results

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 $alpha$ to control the complete pivoting process‎. ‎We have studied the effect of dif...

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 ...

Multilevel Preconditioners Constructed From Inverse-Based ILUs

This paper analyzes dropping strategies in a multilevel incomplete LU decomposition context and presents a few of strategies for obtaining related ILUs with enhanced robustness. The analysis shows that the Incomplete LU factorization resulting from dropping small entries in Gaussian elimination produces a good preconditioner when the inverses of these factors have norms that are not too large. ...

Certain Sums Involving Inverses of Binomial Coefficients and Some Integrals

In this paper, we are concerned with sums involving inverses of binomial coefficients. We study certain sums involving reciprocals of binomial coefficients by using some integrals. Some recurrence relations related to inverses of binomial coefficients are obtained. In addition, we give the approximate values of certain sums involving the inverses of binomial coefficients.