This paper is concerned with a new approach for preconditioning large sparse least squares problems. Based on the idea of the approximate inverse preconditioner, which was originally developed for square matrices, we construct a generalized approximate inverse (GAINV)M which approximately minimizes ∥/ −M A∥F or ∥I −AM∥F. Then, we also discuss the theoretical issues such as the equivalence between the original least squares problem and the preconditioned problem. Finally, numerical experiments on problems from Matrix Market collection and random matrices show that although the preconditioning is expensive, it pays off in certain cases.

中文翻译：

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最小二乘问题的广义近似逆预处理器

本文涉及一种预处理大型稀疏最小二乘问题的新方法。基于最初为方阵开发的近似逆预处理器的思想，我们构造了一个广义近似逆 (GAINV)M，它近似最小化 ∥/ −MA∥F 或 ∥I −AM∥F。然后，我们还讨论了原始最小二乘问题和预处理问题之间的等价性等理论问题。最后，对矩阵市场集合和随机矩阵问题的数值实验表明，尽管预处理很昂贵，但在某些情况下还是有回报的。