Simultaneous preconditioning and symmetrization of non-symmetric linear systems

2008/01/25 by Nassif Ghoussoub, Amir Moradifam, Ghoussoub, Nassif +1
Computer Science · Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.0801.3865

openalex publication_date 2008/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Motivated by the theory of self-duality which provides a variational formulation and resolution for non self-adjoint partial differential equations \citeG1, G2, we propose new templates for solving large non-symmetric linear systems. The method consists of combining a new scheme that simultaneously preconditions and symmetrizes the problem, with various well known iterative methods for solving linear and symmetric problems. The approach seems to be efficient when dealing with certain ill-conditioned, and highly non-symmetric systems.

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