| 一类二次矩阵方程的条件数和后向误差 |
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| 引用本文： | 刘兰冬.一类二次矩阵方程的条件数和后向误差[J].应用数学与计算数学学报,2014(4):424-431. |
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| 作者姓名： | 刘兰冬 |
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| 作者单位： | 中国矿业大学(北京)理学院,北京100083 |
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| 基金项目： | 国家自然科学基金资助项目（11371364）;中央高校基本科研业务费资助项目（2009QS09） |
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| 摘 要： | 主要讨论一类二次矩阵方程X^2-EX-F=0的条件数和后向误差,其中E是一个对角矩阵,F是一个M矩阵.这类二次矩阵方程来源于Markov链的噪声Wiener-Hopf问题.实际问题中人们感兴趣的是它的M矩阵的解.应用Rice创立的基于Frobenius范数下的条件数理论,导出此类二次矩阵方程的M矩阵解的条件数的显式表达式.同时,也给出近似解的后向误差的定义以及一个可计算的表达式.最后,通过数值例子验证理论结果是有效的.
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| 关 键 词： | 二次矩阵方程 M-矩阵 扰动分析 条件数 后向误差 |
Condition number and backward error of quadratic matrix equation |
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| LIU Lan-dong.Condition number and backward error of quadratic matrix equation[J].Communication on Applied Mathematics and Computation,2014(4):424-431. |
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| Authors: | LIU Lan-dong |
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| Institution: | LIU Lan-dong(College of Sciences, China University of Mining and Technology, Beijing 100083, China) |
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| Abstract: | This paper is devoted to the condition number and backward error for the quadratic matrix equation X~2- EX- F = 0,where E is a diagonal matrix and F is an M-matrix.The quadratic matrix equation of this type arises in noisy Wiener-Hopf problems for Markov chains.The solution of the practical interest is a particular M-matrix solution.We apply the condition number theory developed by Rice to define the condition number in the Frobenius norm.The explicit expression of the condition number is derived in a uniform manner.Meanwhile,the backward error is defined and evaluated by an explicit formula.The theoretical results are illustrated by using the simple numerical examples. |
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| Keywords: | quadratic matrix equation M-matrix perturbation analysis condition number backward error |
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