求解对称区间矩阵标准特征值的进化策略新算法  

A Novel Evolution Strategy Algorithm for Solving the Standard Eigenvalue of the Symmetric Interval Matrix

作　　者：夏慧明[1] 周永权[2] 

机构地区：[1]南京师范大学泰州学院数学科学与应用学院,山东泰州225300 [2]广西民族大学数学与计算机科学学院,广西南宁530006

出　　处：《计算机工程与科学》2011年第2期97-101,共5页Computer Engineering & Science

基　　金：国家自然科学基金资助项目(60461001);广西自然科学基金资助项目(0542048);广西研究生教育创新计划资助项目(2007106080701M18);广西民族大学重大项目资助课题

摘　　要：针对实对称区间矩阵的特征值问题,将区间不确定量看成是围绕区间中点的一种摄动,提出了一种基于区间扩张的对称区间矩阵特征值问题求解的进化策略算法。将区间矩阵中点作为平衡点,区间不确定量作为相应的扰动量,根据摄动公式求出区间矩阵的最大特征值和最小特征值,从而获得区间矩阵特征值问题的解。算例显示了该算法的有效性,其主要特点是收敛速度快、求解区间精度高。For the eigenvalue problem of real symmetric interval matrixes, the uncertainties of the interval are thought as one perturbed quantity around the midpoint of the interval. In this paper an Evolution Strategy Algorithm is presented for solving the eigenvalue problem of interval matrixes based on the expansion of the interval. Taking the center point of the interval matrix as the balancing point and the interval indefinite quantity as the perturbation quantity, the solving the minimum and maximum eigenvalues of the interval matrix by perturbation formulas, the solution of the eigenvalue problem is obtained. The example which is given in the article has illustrated that the algorithm is effective. The main feature of the algorithm is that the result region is very accurate and the convergence speed is fast.

关 键 词：区间矩阵 特征值 矩阵摄动 区间摄动 进化策略 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]