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On relaxed greedy randomized coordinate descent methods for solving large linear least-squares problems
Applied Numerical Mathematics ( IF 2.8 ) Pub Date : 2020-11-01 , DOI: 10.1016/j.apnum.2020.06.014
Jianhua Zhang , Jinghui Guo

Abstract The greedy randomized coordinate descent (GRCD) method is an effective iterative method for solving large linear least-squares problems. In this work, we construct a class of relaxed greedy randomized coordinate descent (RGRCD) methods by introducing a relaxation parameter in the probability criterion. Then, we prove the convergence properties of these methods when the coefficient matrix of the linear least-squares problems is of full column rank, with the number of rows being no less than the number of columns. In addition, we propose a max-distance coordinate descent (CD) method, and study its convergence properties and accelerated version. Finally, we provide some numerical experiments to confirm the effectiveness of our new methods.

中文翻译:

求解大型线性最小二乘问题的宽松贪婪随机坐标下降法

摘要 贪心随机坐标下降(GRCD)方法是求解大型线性最小二乘问题的有效迭代方法。在这项工作中,我们通过在概率标准中引入松弛参数来构建一类松弛贪婪随机坐标下降(RGRCD)方法。然后,我们证明了当线性最小二乘问题的系数矩阵为满列秩且行数不小于列数时这些方法的收敛性。此外,我们提出了一种最大距离坐标下降(CD)方法,并研究了其收敛特性和加速版本。最后,我们提供了一些数值实验来证实我们新方法的有效性。
更新日期:2020-11-01
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