预处理P＝（I＋C）后双分裂下的S OR迭代法收敛性

摘要

针对预处理方法求解大型稀疏线性方程组Ax ＝b ，在以往选择预处理因子的基础上，结合矩阵分析、分裂理论，给出不同以往的两种预处理后含参数形式的SOR迭代方法分裂形式，证明新分裂形式能够使SOR迭代法收敛，并得到收敛速度优于一般的预处理方法，最后找到参数的最优取值。%For iterative method to solving the linear system Ax=b in the preconditioned,on the basis of selecting the preconditioned factors in the past by using matrix iterative analysis and comparison theo-rems,two types of the split form with parameters are given.The new splitting methods not only can make the SOR iterative method convergence,but also can make the convergence rate better than the general preconditioned SOR method,and finally find the optimal values of the parameters.