改进矩阵分裂形式的预条件SOR迭代法收敛性讨论

Discussion of Convergence for Preconditioned SOR Iterative Method Based on Improved Matrix Splitting Modus

结合矩阵分裂理论及比较定理,给出一种改进矩阵分裂形式的预条件含参数SOR迭代方法,证明这种方法不仅能加速SOR迭代法的收敛性,而且优于一般的预条件方法,并找出了参数的最优取值。最后通过数值例子进行了说明。

The author studies the preconditioned iterative method for solving the linear system Ax=b.Jae Heon Yun discussed the P=（I＋C） to accelerate convergence of SOR iterative method.In this paper,an improved SOR iterative method is employed by using matrix iterative analysis and comparison theorems to solve the large linear system preconditioned based on matrix splitting.The improved method is proved not only to be able to accelerate the SOR iterative method,but also to excel the general preconditioned SOR method.At last,numerical example is given.