Multilayer approximate nullspace methods for saddle point systems

TL;DR

This paper introduces a novel multi-layer iterative scheme for efficiently solving sparse saddle point linear systems, combining nullspace-based preconditioning with iterative least squares and projection methods, supported by theoretical analysis and practical testing.

Contribution

It presents a new multi-layer iterative scheme that integrates nullspace methods with least squares and projection techniques for saddle point systems.

Findings

Effective and robust on various sparse matrices

Theoretical analysis supports convergence and stability

Demonstrated improvements over existing methods

Abstract

We propose a new class of multi-layer iterative schemes for solving sparse linear systems in saddle point structure. The new scheme consist of an iterative preconditioner that is based on the (approximate) nullspace method, combined with an iterative least squares approach and an iterative projection method. We present a theoretical analysis and demonstrate the effectiveness and robustness of the new scheme on sparse matrices from various applications.