幂平均牛顿法求解方程的重根

Power Mean Newton's Method for Multiple Roots

讨论用建立在幂平均基础上的牛顿法求解方程的多重根的收敛性问题,证明了用此方法求解方程重根是线性收敛的,并且若知道了根的重数,可改进其迭代公式使其二阶收敛,同时该文结论部分说明了用幂平均牛顿法求解方程的多重根时,幂指数越小,收敛速度越快。

In this paper,the convergence behavior of power mean Newton's for multiples roots been shown.Using this method,it converges linearly to multiple roots and if we known the multiplicity,it converges quadratically to multiple roots,Moreover,it is shown that if you using this method to get the multiple roots of nonlinear equation,its power exponent should be smaller,then it can convergent more quickly.