标题： 多项式方程多重根的Obreshkoff-Ehrlich方法的推广 显示英文标题

标题： A Generalization of Obreshkoff-Ehrlich Method for Multiple Roots of Polynomial Equations

摘要： 在本文中，我们开发了一种新方法，它是Obreshkoff-Ehrlich方法的推广，适用于代数、三角和指数多项式的情况。该方法具有三次收敛速度。从计算角度来看，它很有效，并且可以用于同时找到所有根，如果已知根的重数的话。尽管重数是任意的，但这种方法的复杂度与用于同时找到简单根的方法相同。我们不使用带有多个节点的差商，这一事实不会导致计算给定多项式的高阶导数，而只涉及一阶导数。 显示英文摘要

摘要： In this paper we develop a new method which is a generalization of the Obreshkoff -Ehrlich method for the cases of algebraic, trigonometric and exponential polynomials. This method has a cubic rate of convergence. It is efficient from the computational point of view and can be used for simultaneous finding all roots if the roots have known multiplicities. This new method in spite of the arbitrariness of multiplicities is of the same complexity as the methods for simultaneous finding all roots of simple roots. We do not use divided differences with multiple knots and this fact does not lead to calculation of derivatives of the given polynomial of higher order, but only of first ones.