| 二次四元数系统正定解的迭代法 |
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| 引用本文： | 黄敬频,张姗姗,熊,昊.二次四元数系统正定解的迭代法[J].应用数学,2021,34(2):357-364. |
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| 作者姓名： | 黄敬频 张姗姗 熊 昊 |
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| 作者单位： | 广西民族大学数学与物理学院, 广西 南宁 530006 |
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| 基金项目： | 国家自然科学基金项目(11661011);广西民族大学研究生创新项目(gxun-chxps2020)。 |
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| 摘 要： | 二次四元数系统XAX?BX=P是离散型Lyapunov方程正定解反问题的推广形式.本文在四元数体上讨论它的正定解存在性及迭代求解方法.利用等价二次方程的系数矩阵的极大极小特征值,获得其正定解的存在区间,并针对系数矩阵的不同情况构建出三种收敛的迭代格式.同时根据每种迭代的特点,给出了迭代初始矩阵的选取方法.最后通过四元数矩阵复算子实现Matlab环境下求解.数值算例验证了所给方法的有效及可行性.
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| 关 键 词： | 二次四元数系统 正定解 存在性 迭代法 |
| 收稿时间： | 2020/4/16 0:00:00 |
Iterative Methods of the Positive Definite Solution to a Quadratic Quaternion System |
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| HUANG Jingpin,ZHANG Shanshan,XIONG Hao.Iterative Methods of the Positive Definite Solution to a Quadratic Quaternion System[J].Mathematica Applicata,2021,34(2):357-364. |
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| Authors: | HUANG Jingpin ZHANG Shanshan XIONG Hao |
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| Institution: | (School of Mathematics and Physics,Guangxi University for Nationalities,Nanning 530006,China) |
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| Abstract: | The quadratic quaternion system XAX?BX=P is actually a generalized form of the inverse problem on discrete Lyapunov equation.In this paper,the existence of the positive definite solution and its iterative algorithm of the system are discussed.The existence interval of positive solutions of the system is obtained by largest and smallest eigenvalues of coefficient matrices to an equivalent quadratic equation,and three iterative formulas and convergence criteria are found.Meanwhile,the methods of selecting initial matrix are given according the features of each iteration.Finally,It is realizes solving the system in matlab environment by complex operator of a quaternion matrix.A simulation example is given to illustrate the validity and feasibility of the methods. |
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| Keywords: | Quadratic quaternion system Positive definite solution Existence Iterative method |
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