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 ...

We have developed a highly parallel sparse Cholesky factorization algorithm that substantially improves the state of the art in parallel direct solution of sparse linear systems—both in terms of scalability and overall performance. It is a well known fact that dense matrix factorization scales well and can be implemented efficiently on parallel computers. However, it had been a challenge to dev...

We extend some results of Brewer and Heinzer about integral domains with certain comaximal factorization properties for ideals, to the more general setup multiplicative lattices.

Torsion theories are here extended to categories equipped with an ideal of 'null morphisms', or equivalently a full subcategory of 'null objects'. Instances of this extension include closure operators viewed as generalised torsion theories in a 'category of pairs', and factorization systems viewed as torsion theories in a category of morphisms. The first point has essentially been treated in [15].