求解矩阵特征值的改进PSO算法

为了改进粒子群算法在求解矩阵特征值时只能根据矩阵特征值范围逐一求解特征值的现状。提出了一种改进的粒子群算法。改进的粒子群算法采用寻找到一个特征值后,适当改变适应值函数的策略,使搜索区域远离已寻找到的特征值,继续寻找其他的特征值,如此反复,直到寻找到所有的特征值为止。利用四个不同类型的矩阵求解特征值进行仿真,实验结果也验证了算法的实用性和有效性。

Modified PSO algorithm for solving matrix eigenvalues

To improve the situation that eigenvalue of matrix is gained one-by-one through the application of Particle Swarm Optimiza- tion, a new kind of Particle Swarm Optimization is proposed. The modified Particle Swarm Optimization probably changes the fitness function after one eigenvalue is gained. Through this strategy, all the eigenvalues of a matrix will be got through one application of Par- ticle Swarm Optimization. Simulation experiment with four kinds of matrix shows the practicality and effectiveness of the modified Par- title Swarm Optimization.