HSS迭代算法在求解矩阵最小特征时的应用

Application of HSS iterative algorithm in solving minimum eigenvalue of matrix

为了更加精确快速地求解M-矩阵线性方程组,引入了HSS迭代算法.利用了M-矩阵的特点,在反幂法的基础上采用了改进的算法,并在实际运算的过程中引入HSS迭代算法.在此基础上采用了HSS迭代方法,并将此算法拓展到了M-矩阵之中,并且证明了其收敛性.给定了矩阵在求解最小特征值时α的取值,并通过算例验证了该算法在应用于求解最小特征值时的可行性.

In order to solve M-matrix linear equations more accurately and quickly,this paper introdued a HSS iterative algorithm.And used the characteristics of the M-matrix,and improved the algorithm based on the inverse iteration.Actually introduced an HSS iterative algorithm in the actual calculation process.Based on this,a HSS iterative method was adopted.And extend this algorithm into matrix and proved its convergence.Given a proper value ofαin the matrix when solving the minimum eigenvalue,the feasibility of the algorithm in solving the minimum eigenvalue was verified by an example.