| 求解一类非线性矩阵方程的无逆迭代法 |
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| 引用本文： | 陈争,马昌凤.求解一类非线性矩阵方程的无逆迭代法[J].平顶山学院学报,2014(2):1-5. |
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| 作者姓名： | 陈争 马昌凤 |
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| 作者单位： | 福建江夏学院数理教研部;福建师范大学数学与计算机科学学院 |
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| 基金项目： | 国家自然科学基金(11071041);福建省自然科学基金(2013J01006) |
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| 摘 要： | 提出了求非线性矩阵方程X+ATX-1A+BTX-1B=Q最大正定解的一个无逆迭代法.证明了由该算法产生的迭代序列单调递增有上界且收敛于原方程的最大正定解.数值实验表明该算法是十分有效的.
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| 关 键 词： | 非线性矩阵方程 无逆迭代法 最大正定解 收敛性 数值实验 |
Solution to a Class of Nonlinear Matrix Equation with Inversion-free Iterative Method |
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| CHEN Zheng;MA Changfeng.Solution to a Class of Nonlinear Matrix Equation with Inversion-free Iterative Method[J].Journal of Pingdingshan University,2014(2):1-5. |
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| Authors: | CHEN Zheng;MA Changfeng |
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| Institution: | CHEN Zheng;MA Changfeng;Department of Mathematics and Physics,Fujian Jiangxia University;School of Mathematics and Computer Science,Fujian Normal University; |
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| Abstract: | This paper presents the maximal positive definite solution of the nonlinear matrix equation X ＋ A^TX^-1A ＋ B^TX^-1B = Q with an inversion-free iterative method,and proves that the sequences generated by the iterative schemes are monotonically increasing and weakening above. Numerical experiments further show the effectiveness of the new methods. |
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| Keywords: | nonlinear matrix equation inversion-free iterative method maximal positive definite solution convergence analysis numerical experiment |
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