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arXiv · 2502.17626

Preconditioned normal equations for solving discretised partial differential equations

Lorenzo Lazzarino·Yuji Nakatsukasa·Umberto Zerbinati
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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.

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Lorenzo Lazzarino, Yuji Nakatsukasa, Umberto Zerbinati. 2025-02-24. Preconditioned normal equations for solving discretised partial differential equations. https://arxiv.org/abs/2502.17626

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