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.

翻译：本文探讨针对偏微分方程离散化产生的非对称方阵线性系统，预处理其法向方程的方法，重点关注CGNE和LSQR等算法。文中提出了“法向”预处理的概念，并给出一种通过研究关联“法向”偏微分方程来构造预处理子的策略。对流-扩散问题的数值实验表明，该方法能有效实现快速且稳定的收敛。