标题： 用于高效大矩阵求逆的蒙特卡罗算法 显示英文标题

标题： A Monte Carlo algorithm for efficient large matrix inversion

摘要： 本文介绍了一种新的蒙特卡洛算法来求解大型矩阵的逆矩阵。 该算法基于从两个随机向量中同时耦合抽样的方法，其协方差即为所需的逆矩阵。 可以将其视为之前报道的一种仅基于一次抽样的厄米矩阵逆矩阵算法的推广。 使用两次抽样使得非厄米矩阵的逆矩阵成为可能。 收敛条件和收敛速率与高斯-赛德尔算法类似。 给出了两个示例的结果，一个是与数量遗传学相关的实非对称矩阵，另一个是物理学家关注的复非厄米矩阵。 与其他蒙特卡洛算法相比，它显示出处理时间的大幅减少，在所研究的示例中处理速度提高了八倍。 显示英文摘要

摘要： This paper introduces a new Monte Carlo algorithm to invert large matrices. It is based on simultaneous coupled draws from two random vectors whose covariance is the required inverse. It can be considered a generalization of a previously reported algorithm for hermitian matrices inversion based in only one draw. The use of two draws allows the inversion on non-hermitian matrices. Both the conditions for convergence and the rate of convergence are similar to the Gauss-Seidel algorithm. Results on two examples are presented, a real non-symmetric matrix related to quantitative genetics and a complex non-hermitian matrix relevant for physicists. Compared with other Monte Carlo algorithms it reveals a large reduction of the processing time showing eight times faster processing in the examples studied.