We recently introduced a sparse stretching strategy for handling dense rows that can arise in large-scale linear least-squares problems and make such problems challenging to solve. Sparse stretching is designed to limit the amount of fill within the stretched normal matrix and hence within the subsequent Cholesky factorization. While preliminary results demonstrated that sparse stretching performs significantly better than standard stretching, it has a number of limitations. In this article, we discuss and illustrate these limitations and propose new strategies that are designed to overcome them. Numerical experiments on problems arising from practical applications are used to demonstrate the effectiveness of these new ideas. We consider both direct and preconditioned iterative solvers.

中文翻译：

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一些密集行的最小二乘问题的拉伸的优点和局限性

我们最近引入了一种稀疏拉伸策略，用于处理大规模线性最小二乘问题中可能出现的密集行，并使此类问题难以解决。稀疏拉伸旨在限制拉伸法线矩阵内的填充量，从而限制随后的 Cholesky 分解。虽然初步结果表明稀疏拉伸的性能明显优于标准拉伸，但它有许多局限性。在本文中，我们讨论并说明了这些限制，并提出了旨在克服这些限制的新策略。对实际应用中出现的问题进行数值实验来证明这些新想法的有效性。我们考虑直接和预处理迭代求解器。