| Stein方程数值解的黎曼梯度算法 |
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| 引用本文： | 段晓敏,赵新玉,孙华飞. Stein方程数值解的黎曼梯度算法[J]. 北京理工大学学报, 2016, 36(2): 201-204. DOI: 10.15918/j.tbit1001-0645.2016.02.018 |
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| 作者姓名： | 段晓敏 赵新玉 孙华飞 |
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| 作者单位： | 大连交通大学材料科学与工程学院,辽宁,大连116028;大连交通大学理学院,辽宁,大连116028;大连交通大学材料科学与工程学院,辽宁,大连116028;北京理工大学数学学院,北京,100081 |
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| 基金项目： | 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) |
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| 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.
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| 关 键 词： | Stein方程 黎曼梯度算法 数值模拟 |
| 收稿时间： | 2015-07-03 |
Riemannian Gradient Algorithm for the Numerical Solution of Stein Equations |
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| DUAN Xiao-min,ZHAO Xin-yu and SUN Hua-fei. Riemannian Gradient Algorithm for the Numerical Solution of Stein Equations[J]. Journal of Beijing Institute of Technology(Natural Science Edition), 2016, 36(2): 201-204. DOI: 10.15918/j.tbit1001-0645.2016.02.018 |
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| Authors: | DUAN Xiao-min ZHAO Xin-yu SUN Hua-fei |
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| Affiliation: | 1.School of Science, Dalian Jiaotong University, Dalian, Liaoning 116028, China;School of Materials Science and Engineering, Dalian Jiaotong University, Dalian, Liaoning 116028, China2.School of Science, Dalian Jiaotong University, Dalian, Liaoning 116028, China3.Mathematical School, Beijing Institute of Technology, Beijing 100081, China |
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| Abstract: | 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. |
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| Keywords: | Stein equation Riemannian gradient algorithm simulation |
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