中文摘要：

讨论了求解非线性方程重根问题，针对此时Moore区间牛顿法不再适用，以及Hansen改进的区间牛顿法收敛速度慢的情况，通过引入原方程的一种相关方程，建立了求解非线性方程重根的区间牛顿法；证明了其局部平方收敛的性质，给出了数值算例。验证了新算法比Hansen改进的区间牛顿法具有更快的收敛速度，且算法是有效和可靠的。

英文摘要：

Nonlinear equations for solving the roots are discussed, for the interval Newton method is no longer applicable and the convergence of the improved interval Newton method is so slow, by introducing a correlative equation, a new improved interval Newton method for solving the roots of nonlinear equations is established. Its local quadratic convergence property is proved, numerical examples are given. That the new method has faster conver- gence speed than the improved interval Newton method is verified, and it is effective and reliable.