遗传算法在矩阵特征值求解中的应用

The Application of the Genetic Algorithms to Solution to Matrix Eigenvalue

讨论了矩阵及其特征值的一些性质,得出了最大特征值下界的两个定理。依据定理的结论可以确定矩阵的最大特征值的上下界,从而可以对遗传算法进行编码。基于遗传算法求得矩阵的最大特征值,并且跟幂法进行比较,得到了较好的结果。遗传算法不受特征值结构条件限制,能很快找到最优解,比传统搜索算法更加灵活。

We will discuss some characters of matrix and its eigenvalue. Based on the demonstration, we get to final conclusions of the lower boundary in maximum eigenvalue. According to the genetic algorithms, we can find the maximum eigenvalue of matrix. With genetic algorithms compared with the power method, a better result is gained. It doesn＇t confine to the condition of eigenvalue structure and easily to find the best solution. It is more flexible than the traditional method.