带加速因子的线性方程组通用性迭代法的讨论

Discussion on General Iteration Method with Accelerated Factor for Linear Equations

在带加速因子的线性方程组通用性迭代解法的基础上,用几何方法对加速因子进行了讨论,证明了每次迭代中最佳加速因子的存在性,讨论了在每次迭代中使算法收敛的加速因子的取值范围,设计了一个动态调整加速因子的通用性迭代算法,并进行了程序验证.

Based on general iteration method with accelerated factor for linear equations,the accelerated factor is discussed by using geometrical method.It is proved that the best accelerated factor of every iteration is existent.Moreover the accelerated factor range in which the iteration is convergent is also discussed.Finaly,a general iteration method with dynamic adjusting accelerated factor is designed and checked.