Preconditioning with direct approximate factoring of the inverse

2012/08/17 by Mikko Byckling, Byckling, Mikko, Marko Huhtanen +1
Computer Science · Engineering · Physics and Astronomy · #65F05 #65F10 #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1208.3573

openalex publication_date 2012/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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