摘要
基于正定矩阵流形的信息几何结构,使用黎曼梯度算法来获得Stein方程的数值解.利用弯曲的黎曼流形上的测地距离作为算法的目标函数,并将流形上的测地线作为算法的收敛路径.通过数值实验讨论了算法的步长和收敛速度的关系,从而得到算法的最优步长.
A Riemannian gradient algorithm based on information geometric structures of a manifold consisting of all symmetric positive-definite matrices was proposed to calculate the numerical solution of Stein equations.In this algorithm,the geodesic distance on the curved Riemannian manifoldis taken as an objective function and the geodesic curve was treated as the convergence path.Also the optimal variable step-sizes corresponding to the minimum value of the objective function were provided in order to improve the convergence speed.
出处
《北京理工大学学报》
EI
CAS
CSCD
北大核心
2016年第2期201-204,共4页
Transactions of Beijing Institute of Technology
基金
国家自然科学基金资助项目(61401058
61179031)
中国博士后科学基金面上资助项目(2015M581323)
