论文标题
通过正交化贪婪的双子空间协调下降法
Greedy double subspaces coordinate descent method via orthogonalization
论文作者
论文摘要
坐标下降方法是解决大型线性最小二乘问题的有效迭代方法。在本文中，对于高度连贯的列情况，我们构建了一种有效的坐标下降方法，该方法将估计值迭代地将估计值投射到两个贪婪选择的超平面通过革兰氏式正交化形成的解决方案空间上。我们的方法可以被视为涉及两个活动列的坐标下降方法的简单块版。提供了此方法的收敛分析，数值模拟还确认了具有高度连贯柱的矩阵的有效性。
The coordinate descent method is an effective iterative method for solving large linear least-squares problems. In this paper, for the highly coherent columns case, we construct an effective coordinate descent method which iteratively projects the estimate onto a solution space formed by two greedily selected hyperplanes via Gram-Schmidt orthogonalization. Our methods may be regarded as a simple block version of coordinate descent method which involves two active columns. The convergence analysis of this method is provided and numerical simulations also confirm the effectiveness for matrices with highly coherent columns.
