论文标题
在用于求解线性最小二乘问题问题的扩展随机多行方法上
On the extended randomized multiple row method for solving linear least-squares problems
论文作者
论文摘要
随机行方法是迭代算法的流行代表，因为它在求解线性方程的过度确定和一致的系统方面具有效率。在本文中，我们提出了一种扩展的随机多行方法，以解决给定的过度确定和不一致的线性系统，并在每次迭代时分析其计算复杂性。我们证明，所提出的方法可以用最小的欧几里得规范在均方根中线性收敛至最小二乘溶液。提出了几项数值研究以证实我们的理论发现。还提供了用于插图目的的计算机辅助几何设计中的现实世界应用，例如图像重建和大型噪声数据拟合。
The randomized row method is a popular representative of the iterative algorithm because of its efficiency in solving the overdetermined and consistent systems of linear equations. In this paper, we present an extended randomized multiple row method to solve a given overdetermined and inconsistent linear system and analyze its computational complexities at each iteration. We prove that the proposed method can linearly converge in the mean square to the least-squares solution with a minimum Euclidean norm. Several numerical studies are presented to corroborate our theoretical findings. The real-world applications, such as image reconstruction and large noisy data fitting in computer-aided geometric design, are also presented for illustration purposes.
