A two-level iterative scheme for general sparse linear systems based on approximate skew-symmetrizers

TL;DR

This paper introduces a novel two-level iterative method utilizing approximate skew-symmetrizers and a specialized minimal residual method to efficiently solve general sparse linear systems, enhancing robustness and convergence.

Contribution

It presents a new two-level iterative scheme with a skew-symmetrizer-based preconditioner and a tailored minimal residual method for shifted skew-symmetric systems, improving solution robustness.

Findings

Demonstrates robustness across various sparse matrices

Achieves efficient convergence with the proposed preconditioner

Provides a practical approach for large sparse systems

Abstract

We propose a two-level iterative scheme for solving general sparse linear systems. The proposed scheme consists of a sparse preconditioner that increases the skew-symmetric part and makes the main diagonal of the coefficient matrix as close to the identity as possible. The preconditioned system is then solved via a particular Minimal Residual Method for Shifted Skew-Symmetric Systems (mrs). This leads to a two-level (inner and outer) iterative scheme where the mrs has short term recurrences and satisfies an optimally condition. A preconditioner for the inner system is designed via a skew-symmetry preserving deflation strategy based on the skew-Lanczos process. We demonstrate the robustness of the proposed scheme on sparse matrices from various applications.