牛顿法的二项式展开
Binomial expansion of Newton's method
摘要：
我们推广了牛顿法，并证明了推广的牛顿法导致了牛顿法的二项式展开，使收敛性变为二次和线性。在平方收敛的情况下，给出了牛顿法和牛顿法的二项式展开式的收敛性比较。并利用曲线的曲率和凹凸性对牛顿法和牛顿法的二项式展开式的收敛性进行了比较。接下来我们给出牛顿法的二项式展开的数值计算的例子。
英文摘要：
We extend the Newton's method and show the extended Newton's method leads to the binomial expansion of Newton's method that the convergences become the quadratic and linearly. In case of the quadratic convergence, we give the convergence comparison of the binomial expansion of Newton's method and Newton's method. And we give convergence comparisons of the binomial expansion of Newton's method and Newton's method using the curvature and convex-concave of curve. Next we give examples of numerical calculations of the binomial expansion of Newton's method.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
