Strengths and Limitations of Stretching for Least-squares Problems with Some Dense Rows
Strengths and Limitations of Stretching for Least-squares Problems with Some Dense Rows
复制标题
具有某些密集行的最小二乘问题的拉伸的优点和局限性
DOI：
10.1145/3412559
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
M. Tuma
中科院分区：
文献类型：
--
作者：
J. Scott;M. Tuma
我们最近引入了一种稀疏拉伸策略来处理大规模线性最小二乘问题中可能出现的密集行，这使得此类问题的解决具有挑战性。稀疏拉伸旨在限制拉伸的法线矩阵中的填充量，从而限制后续的Cholesky因式分解。虽然初步结果表明，稀疏拉伸的效果明显好于标准拉伸，但它也有一些局限性。在本文中，我们将讨论和说明这些限制，并提出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了数值实验，验证了这些新思想的有效性。我们同时考虑直接迭代求解器和预条件迭代求解器。
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.