| 求解Sylvester矩阵方程的一种改进的梯度方法 |
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| 引用本文： | 顾传青,蒋祥龙.求解Sylvester矩阵方程的一种改进的梯度方法[J].应用数学与计算数学学报,2014(4):432-439. |
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| 作者姓名： | 顾传青 蒋祥龙 |
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| 作者单位： | 上海大学理学院,上海200444 |
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| 基金项目： | 国家自然科学基金资助项目（11371243）;上海市教委科研创新重点资助项目（13ZZ068）;上海市重点学科建设资助项目（S30104） |
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| 摘 要： | 提出了一种改进的梯度迭代算法来求解Sylvester矩阵方程和Lyapunov矩阵方程.该梯度算法是通过构造一种特殊的矩阵分裂,综合利用Jaucobi迭代算法和梯度迭代算法的求解思路.与已知的梯度算法相比,提高了算法的迭代效率.同时研究了该算法在满足初始条件下的收敛性.数值算例验证了该算法的有效性.
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| 关 键 词： | 梯度迭代算法 Jacobi梯度迭代算法 Sylvester方程 Lyapunov矩阵方程 |
Improved gradient iteration algorithm for solving Sylvester matrix equations |
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| GU Chuan-qing,JIANG Xiang-long.Improved gradient iteration algorithm for solving Sylvester matrix equations[J].Communication on Applied Mathematics and Computation,2014(4):432-439. |
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| Authors: | GU Chuan-qing JIANG Xiang-long |
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| Institution: | (College of Sciences, Shanghai University, Shanghai 200444, China) |
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| Abstract: | An improved gradient iteration algorithm to solve Sylvester matrix equations and Lyapunov matrix equations is proposed.Based on the ideas of the Jacobi iteration algorithm and the gradient iteration algorithm,a new algorithm is constructed by using a kind of matrix splitting method.By comparing with existing algorithms,the new method improves the efficiency of the iteration.At the same time,the convergence of the algorithm is proved and a numerical example is given to illustrate. |
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| Keywords: | gradient iterative algorithm Jacobi gradient iterative algorithm Sylvester matrix equation Lyapunov matrix equation |
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