计算区间特征值的Rayleigh商法

A fast method for computing eigenvalues of a structural matrix with interval parameters

为提高区间特征值的计算效率,首先分析了区间结构矩阵特征值的设计变量的单调性问题,随后采用区间因子法给出了基于Rayle igh商计算结构广义特征值的一种快速算法。当诸参数的变化区间相对其均值的离差较小时,区间结构矩阵特征值的计算精度主要由各区间因子的差值大小所决定;且当各区间因子的差值为零时,误差亦为零。最后给出的两个算例表明:相对于全局优化算法和区间离散法,该方法具有计算效率高、误差小的特点,具有一定的工程实用价值。

In order to increase computational efficiency of interval eigenvalues,the monotone property of design parameters of a structural matrix was studied firstly.Then a fast methodology for calculating the eigenvalues of the structural matrix with interval parameters was put forward,which was based on the Rayleigh quotient and the theories of the interval mathematics.It is shown that as the deviation of the interval factors of the design parameters are similar and close to unity,the computational error of the fast methodology are determined by the dispersion between the interval factors;and the error comes up to zero if all the interval factors are equal.Finally,two numerical examples were given,they proved that the presented method is more feasible and efficient than the global optimization algorithm and the interval stepped dividing method.