非对称矩阵结构系统固有值分析的广义逆迭代法

本文提出一种求解非对称矩阵结构的固有值的数值方法-通过广义的逆迭代过程把一个大型非对称的二次特征值问题简化为小型的标准特征值问题.算法不涉及复数运算,也不需把n阶的二次问题变换为2n阶的线性问题.迭代是在原n阶规模上进行,从而保持了系统各矩阵稀疏、带状的特点.节省了存储量和计算机时.数值实验表明本方法具有良好的稳定性和精度.

Generalized inverse Iteration Method for Eigenvalue Analysis of Nonsymmetric Matrix Structure Systems

In this paper a numerical method for solution of eigenvalues and corresponding eigenvectors of nonsymmetric matrix structure systems is prop sed.Through the procedure of generalized inverse iteration, a large nonsymmetric quadratic eigenproblem is redused to a small linear one. In the new algorithm, neither the complex manipulations nor the transformation of original n-order quadratic eigenproblem into a 2nd-order linear one are needed. Iterations are performed on the original n-order scale.So banded and sparse properties of the system matrices are preserved, and storage capacity and CPU time can be saved. Numerical experiments show excellent stability and accuracy of the algorithm.