摘要： 提出一种基于粒子群优化算法的求解方法，将线性方程组的求解转化为无约束优化问题加以解决，采用粒子群优化算法求解矩阵特征值和特征向量。仿真实验结果表明，该方法求解精度高、收敛速度快，能够在10代左右收敛，可以有效获得任意矩阵的特征值和特征向量。

关键词: 粒子群优化算法, 特征值, 特征向量, 特征方程

Abstract: A method based on Particle Swarm Optimization(PSO) algorithm is presented, which transfers the equations into a non-constraint optimization problem. The PSO algorithm is used to solve matrix eigenvalues and eigenvectors. Simulation experimental results show the accuracy and the convergence speed of this method is higher, which can converge in about ten generations. It can obtain any matrix eigenvalues and eigenvectors.

Key words: Particle Swarm Optimization(PSO) algorithm, eigenvalues, eigenvectors, characteristic equation

中图分类号: 

• TP311