A Monte Carlo algorithm for efficient large matrix inversion
L. A. Garcia-Cortes and C. Cabrillo
本文介绍了一种新的蒙特卡洛算法来倒置大型矩阵。 它基于来自两个随机向量的同时耦合,其协方差是所需的反向。 它可以被认为是以前报告的基于一个平局的隐士矩阵反转算法的概括。 使用两个平局允许反转在非赫密斯矩阵。 收敛的条件和收敛率都类似于高斯-塞德尔算法。 介绍了两个例子的结果,一个真正的非对称矩阵与定量遗传学有关,一个复杂的非隐密矩阵与物理学家有关。 与其他蒙特卡罗算法相比,它揭示了在研究的例子中显示处理速度加快8倍的大大减少。
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...