预处理后多分裂下的SOR迭代法收敛性分析

The Convergence Analysis of the Multi-splitting SOR Iterative Method after Precondition

使用预处理方法解大型线性方程组Ax=b,结合矩阵分裂理论,给出预处理后多种分裂形式的SOR迭代方法,并与一般的预处理方法进行比较分析,证明分裂后的迭代法能加速SOR迭代法的收敛性。最后用数值例子加以验证。

Precondition method is used to solve the large linear systemAx=b in this paper.Combined matrix iterative analysis and comparison theorem,it presents multi-splitting SOR iterative method and compares it with general precondition approach,then proves that the multi-splitting method can not only accelerate the convergence of SOR iterative method,but also surpass the general precondition SOR method.Finally,a numerical example is given.