一种求解矩阵方程 AXB = C 的草图与投影方法
A sketch-and-project method for solving the matrix equation AXB = C
AI总结：
提出一种基于优化问题的草图与投影方法求解矩阵方程 AXB=C，给出收敛速率下界与含秩亏缺情形的收敛条件，并通过参数选择恢复多种已知算法及 GaussGRK，数值实验验证其有效性。
摘要：
本文基于一个优化问题，提出了一种用于求解线性矩阵方程 AXB = C 的草图与投影（sketch-and-project）方法。我们对该新方法进行了全面的收敛性分析，推导了收敛速率的下界以及若干收敛条件，其中包括系数矩阵秩亏缺的情形。通过改变新方法和收敛定理中的三个参数，该新方法可以恢复一系列著名算法及其收敛结果。同时，利用高斯采样，我们可以得到高斯全局随机 Kaczmarz（GaussGRK）方法，该方法在求解矩阵方程 AXB = C 时表现出一定优势。最后，数值实验验证了所恢复方法的有效性。
英文摘要：
In this paper, based on an optimization problem, a sketch-and-project method for solving the linear matrix equation AXB = C is proposed. We provide a thorough convergence analysis for the new method and derive a lower bound on the convergence rate and some convergence conditions including the case that the coefficient matrix is rank deficient. By varying three parameters in the new method and convergence theorems, the new method recovers an array of well-known algorithms and their convergence results. Meanwhile, with the use of Gaussian sampling, we can obtain the Gaussian global randomized Kaczmarz (GaussGRK) method which shows some advantages in solving the matrix equation AXB = C. Finally, numerical experiments are given to illustrate the effectiveness of recovered methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
