不可约L阵下预条件PSD迭代法的敛散性

The divergence theorem of PSD iterative method under irreducible L-matrix

为研究PSD迭代法在不可约L阵下的敛散性,提出一种新的预条件矩阵P=I+S,之后在系数矩阵为没有零元素的L阵的条件下,运用特征向量法比较传统PSD迭代法谱半径与预条件PSD迭代法谱半径的大小,从而得到新的预条件PSD迭代法的敛散性.最后利用数值例子验证了所得结论.

In order to study the convergence of the PSD iterative method under the irreducible L-matrix,a new preconditioned matrix P=I+Sis proposed.Under the condition of the coefficient matrix is not zero element L array,the size of the spectral radius of traditional PSD iterative and the spectral radius of the preconditioned PSD iterative method is compared by using eigenvector method.The divergence of the preconditioned PSD iterative method is obtained.Some numerical examples are given for demonstration.