Preconditioning with direct approximate factoring of the inverse

TL;DR

This paper introduces two parallelizable direct methods for approximate inverse preconditioning of large sparse linear systems, demonstrating improved robustness and flexibility over iterative methods through numerical experiments.

Contribution

It presents novel algorithms for approximate inverse factoring that are fully parallelizable and more robust than existing iterative preconditioners.

Findings

Algorithms are fully parallelizable.

Preconditioners outperform iterative methods in robustness.

Numerical experiments show effectiveness on benchmark systems.

Abstract

To precondition a large and sparse linear system, two direct methods for approximate factoring of the inverse are devised. The algorithms are fully parallelizable and appear to be more robust than the iterative methods suggested for the task. A method to compute one of the matrix subspaces optimally is derived. Possessing a considerable amount of flexibility, these approaches extend the approximate inverse preconditioning techniques in several natural ways. Numerical experiments are given to illustrate the performance of the preconditioners on a number of challenging benchmark linear systems.