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
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摘要: 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。Abstract: 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.