This paper is concerned with a new approach to preconditioning for large sparse linear systems A procedure for computing an incomplete factorization of the inverse of a nonsymmetric matrix is developed and the resulting factorized sparse approximate inverse is used as an explicit preconditioner for conjugate gradient type methods Some theoretical properties of the preconditioner are discussed a...

The combination of iterative methods with preconditionings based on incomplete LU factorizations constitutes an effective class of methods for solving the sparse linear systems arising from the discretization of elliptic partial differential equations. In this paper, we show that there are some settings in which the incomplete LU preconditioners are not effective, and we demonstrate that their ...

Incomplete factorization is one of the most effective general-purpose preconditioning methods for Krylov subspace solvers for large sparse systems of linear equations. Two techniques for enhancing the robustness and performance of incomplete LU factorization for sparse unsymmetric systems are described. A block incomplete factorization algorithm based on the Crout variation of LU factorization ...

For the recursions used in the Modiied Incomplete LU preconditioner (incomplete decomposition , forward elimination and back substitution), a parallelizable approximate solver is presented. It is motivated by an analysis showing that the solutions of these recursions depend only weakly on their initial conditions, which indicates that the solution of a truncated recursion is a fair approximatio...

In this paper, we study the use of an incomplete Cholesky factorization (ICF) as a preconditioner for solving dense symmetric positive definite linear systems. This method is suitable for situations where matrices cannot be explicitly stored but each column can be easily computed. Analysis and implementation of this preconditioner are discussed. We test the proposed ICF on randomly generated sy...

We report on an extensive experiment to compare an iterative solver preconditioned by several versions of incomplete LU factorization with a sparse direct solver using LU factorization with partial pivoting. Our test suite is 24 nonsymmetric matrices drawn from benchmark sets in the literature. On a few matrices, the best iterative method is more than 5 times as fast and more than 10 times as m...

Computational Fluid Dynamics (CID) methods for solving traffic flow continuum models have been studied and efficiently implemented in traffic simulation codes in the past. This is the first time that such methods are studied from the point of view of parallel computing. We studied and implemented an implicit numerical method for solving the high-order flow conservation traffic model on parallel...