求解实对称矩阵区间特征值问题的直接优化法

A Direct Optimization Method for Solving Eigen Problems of Interval Matrices

提出了一种用于对称区间矩阵特征值问题求解的直接优化法。将区间矩阵中为区间量的各元素作为优化设计变量 ,将区间量的分布区间作为相应的设计变量的边界约束 ,运用约束优化法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。本文提出的直接优化法适用于对称区间矩阵的标准特征值问题和广义特征值问题。

A direct optimization method is presented in the paper for solving eigen problems of interval matrices. Taking all the interval entries in the matrices as optimal design varibles and representing the lower and upper bounds of each interval entries as the boundary constraints of the variable respectively, the maximal and the minimal values of the various eigenvalues of the problem are achieved by using the constrained optimization method. That is, the solution of the eigen problem is obtained. The direct optimization method can be used for solving not only normal eigen problems, but also generalized eigen problems of interval matrices. Two examples are presented to illustrate the effectiveness of the direct optimization method.