This article surveys preconditioning techniques for the iterative solution of large linear
systems, with a focus on algebraic methods suitable for general sparse matrices. Covered …

The general method of graph coarsening or graph reduction has been a remarkably useful
and ubiquitous tool in scientific computing and it is now just starting to have a similar impact …

Large linear systems of saddle point type arise in a wide variety of applications throughout
computational science and engineering. Due to their indefiniteness and often poor spectral …

This paper presents a new fine-grained parallel algorithm for computing an incomplete LU
factorization. All nonzeros in the incomplete factors can be computed in parallel and …

We consider bipartite matching algorithms for computing permutations of a sparse matrix so
that the diagonal of the permuted matrix has entries of large absolute value. We discuss …

A number of recently proposed preconditioning techniques based on sparse approximate
inverses are considered. A description of the preconditioners is given, and the results of an …

We present a variant of the AINV factorized sparse approximate inverse algorithm which is
applicable to any symmetric positive definite matrix. The new preconditioner is breakdown …

We propose an incomplete Cholesky factorization for the solution of large-scale trust region
subproblems and positive definite systems of linear equations. This factorization depends on …

When simulating a mechanism from science or engineering, or an industrial process, one is
frequently required to construct a mathematical model, and then resolve this model …

Numerical experiments are presented whereby the effect of reorderings on the convergence
of preconditioned Krylov subspace methods for the solution of nonsymmetric linear systems …