含参数的SOR迭代法收敛性讨论

The convergence discussion of the SOR iterative method with parameter

讨论一类含参数的SOR迭代法求解线性方程组A x=b,得到参数在一定范围内取值时这种方法的收敛性优于一般的SOR迭代法,同时给出参数取不同数值时迭代法谱半径之间的关系,最后给出一个数值例子.

A class of the SOR iterative method with parameter is discussed to solve the large linear system Ax = b. The convergence rate of this new method exceeds the general SOR method. And at the same time this paper obtains the relationship between the spectral radius when the parameters choose different values. At the end, a numerical example is given.