| 二阶线性矩阵差分方程的解及渐近稳定性 |
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| 引用本文： | 黄敬频,黄杭州.二阶线性矩阵差分方程的解及渐近稳定性[J].数学的实践与认识,2009,39(12). |
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| 作者姓名： | 黄敬频 黄杭州 |
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| 作者单位： | 广西民族大学,数学与计算机科学学院,南宁,530006 |
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| 摘 要： | 讨论了二阶线性矩阵差分方程AXn+2+BXn+1+CXn=0的解及其渐近稳定性.首先,给出了它的特征方程有解的一个充要条件,然后利用特征方程两个相异的解刻划出该矩阵差分方程的通解,并分析其解的渐近稳定性,最后运用一实例验证了相关结果.
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| 关 键 词： | 二阶线性矩阵差分方程 特征方程 解 渐近稳定 |
The Solutions of Second Order Linear Matrix Difference Equations and Its Asymptotic Stability |
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| HUANG Jing-pin,HUANG Hang-zhou.The Solutions of Second Order Linear Matrix Difference Equations and Its Asymptotic Stability[J].Mathematics in Practice and Theory,2009,39(12). |
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| Authors: | HUANG Jing-pin HUANG Hang-zhou |
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| Abstract: | We studied the problem about the solutions of second order linear matrix difference equations AXn+2+BXn+1+CXn=0 and its asymptotic stability.Firstly,the necessary and sufficient conditions for the existence a solution of characteristic equation are described,then apply two diverse solutions of characteristic equation to express general solution of the matrix difference equations,and its asymptotic stability are analyzed.Finally,the pertinent results are illustrated by numerical examples. |
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| Keywords: | second order linear matrix difference equations characteristic equation solution asymptotic stability |
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