Preconditioned normal equations for solving discretised partial differential equations
Numerical Analysis
2025-03-03 v2 Numerical Analysis
Abstract
This paper explores preconditioning the normal equation for non-symmetric square linear systems arising from PDE discretization, focusing on methods like CGNE and LSQR. The concept of ``normal'' preconditioning is introduced and a strategy to construct preconditioners studying the associated ``normal'' PDE is presented. Numerical experiments on convection-diffusion problems demonstrate the effectiveness of this approach in achieving fast and stable convergence.
Cite
@article{arxiv.2502.17626,
title = {Preconditioned normal equations for solving discretised partial differential equations},
author = {Lorenzo Lazzarino and Yuji Nakatsukasa and Umberto Zerbinati},
journal= {arXiv preprint arXiv:2502.17626},
year = {2025}
}