试位法的一种改进及其收敛性分析

An Improvement of the Regular Falsi Method and Its Convergence Analysis

摘要: 试位法是用数值方法求单变量非线性方程根的算法，方法简单易行。试位法作为二分法的改进，在大多数情况下优于二分法。本文结合二分法与试位法，给出了试位法的一种改进算法，并对其收敛情况进行了讨论，证明该算法的收敛性，给出了收敛指数的估计。

Abstract: The Regular Falsi method is an algorithm for finding the root of a univariate nonlinear equation by numerical method. The method is simple and easy. The Regular Falsi method is an improvement of the Bisection method and is superior to the Bisection method in most cases. In this paper, an improved algorithm of the test method is given by combining the dichotomy and the test position method. The convergence of the algorithm is proved and the convergence index is estimated.