基于融合邻域寻优与θ-PSO算法的矩阵特征值求解

摘要

Combined neighborhood optimization with θ-PSO algorithm, a new method of solving matrix eigenvalues is presented. The method transfers the problem of solving matrix eigenvalues into the optimization problem. Compared to the other algorithms needing to run for many times, this method can solve all the eigenvalues at one time. The simulation results illustrate the accuracy and the convergence speed of the algorithm is higher, which can converge within about ten to fifteen generations. The algorithm is implemented conveniently, at the same time, it can obtain any matrix eigenvalues. The method can satisfy the accuracy and speed demand completely suitable for application in engineering.%提出一种融合邻域寻优与θ-PSO算法的矩阵特征值求解新方法，将矩阵特征值的求解问题转化为最优化问题。与需要多次运行程序分别求解不同范围的特征值算法相比，该方法可以一次性求出矩阵的全部特征根。仿真实验表明，该算法编程实现方便，对于不同类型的矩阵均可以应用，求解精度高，收敛速度快，大概在10~15代左右就可以收敛，完全可以满足工程实践运算中对精度和速度的要求。