(1,2)相容次序矩阵SOR迭代法的敛散性

The convergence and divergence properties of SOR iterative method for(1,2) consistently ordered matrix

当线性方程组Ax=b的系数矩阵A为(1,2)相容次序矩阵时,将几何和代数方法相结合,讨论了SOR迭代法分别在Jacobi迭代矩阵的所有特征值的3次幂非正和非负情况下的敛散性.最后得到了在Jacobi迭代矩阵所有特征值的3次幂为实数时,SOR迭代法的敛散区间并以实例说明,其中A∈Cn×n,x∈Cn,b∈Cn.

Combining the geometry with the algebra,the convergence and divergence properties of SOR iterative methord are discussed for solving the linear system Ax =b with（1,2）consistently ordered matrix,when all the eigenvalues of the B3J are nonpositive and nonnegative respectively.Finally,the analogous results are provided for the case when all the eigenvalues of the B3J are real,then examples are given to illustrate the results,where BJ is the associated Jacobi iterative matrix,A∈Cn×n,x∈Cn,b∈Cn.