| 非线性矩阵方程数值解的广义哈密顿算法 |
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| 引用本文： | 段晓敏,赵新玉,孙华飞,纪雪婷.非线性矩阵方程数值解的广义哈密顿算法[J].北京理工大学学报,2020,40(2):227-230. |
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| 作者姓名： | 段晓敏 赵新玉 孙华飞 纪雪婷 |
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| 作者单位： | 1. 大连交通大学 理学院, 辽宁, 大连 116028; |
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| 基金项目： | 国家自然科学基金资助项目（61401058）；辽宁省教育厅资助项目（JDL2019013） |
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| 摘 要： | 采用具有近二阶收敛速度的算法计算一类非线性矩阵方程的数值解.根据矩阵方程的解的特征，提出一个基于正定矩阵流形几何结构的广义哈密顿算法.进而比较广义哈密顿算法与经典的多步定常迭代方法的计算行为.最后通过数值模拟表明广义哈密顿算法具有更快的收敛速度.
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| 关 键 词： | 非线性矩阵方程 广义哈密顿算法 数值模拟 |
| 收稿时间： | 2018/12/5 0:00:00 |
An Extended Hamiltonian Algorithm for the Numerical Solution of the Nonlinear Matrix Equation |
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| DUAN Xiao-min,ZHAO Xin-yu,SUN Hua-fei and JI Xue-ting.An Extended Hamiltonian Algorithm for the Numerical Solution of the Nonlinear Matrix Equation[J].Journal of Beijing Institute of Technology(Natural Science Edition),2020,40(2):227-230. |
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| Authors: | DUAN Xiao-min ZHAO Xin-yu SUN Hua-fei and JI Xue-ting |
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| Institution: | 1. School of Science, Dalian Jiaotong University, Dalian, Liaoning 116028, China;2. School of Materials Science and Engineering, Dalian Jiaotong University, Dalian, Liaoning 116028, China;3. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China |
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| Abstract: | In this paper, a second-order learning algorithm was used to solve a class of the nonlinear matrix equations. Specifically, the extended Hamiltonian algorithm was proposed based on manifold of positive definite symmetric matrices. Furthermore, this algorithm was compared with the multi-step iterative method to analyze its operation character. Finally, the simulation results show that, the convergence speed of the extended Hamiltonian algorithm is faster than the traditional algorithm. |
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| Keywords: | nonlinear matrix equation extended Hamiltonian algorithm simulation |
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