使用 Python 比较 Regula Falsi 法、Secant 法和 Bisection 法中非线性方程根的迭代次数

Sabrina Yose Amelia, Diah Aryani, Ary Budi Warsito, Yunianto Purnomo
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引用次数: 0

摘要

求解非线性方程有多种方法,每种方法的迭代次数各不相同。本研究旨在比较 Bisection 法、Regula Falsi 法和 Secant 法在寻找方程根时所需的迭代次数。我们使用 Python 编程语言中的两个不同方程对这三种方法进行了测试。从本研究中的每个方程来看,Bisection 法需要 13 次和 18 次迭代,Regula Falsi 法需要 9 次和 8 次迭代,而 Secant 法需要 5 次迭代。在这三种方法中,正割法所需的迭代次数最少,Regula Falsi 法所需的迭代次数多于正割法,但少于 Bisection 法,而 Bisection 法所需的迭代次数最多。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Comparison of the Number of Iterations of Roots of Non-Linear Equations in the Regula Falsi Method, Secant Method, and Bisection Method using Python
There are several methods for solving nonlinear equations, each method has a different number of iterations. This study aims to compare the number of iterations required by the Bisection, Regula Falsi, and Secant Method in finding the roots of an equation. These three methods were tested using two different equations in the Python programming language. From each equation in this study, Bisection Method requires thirteen and eighteen iterations, Regula Falsi Method requires nine and eight iterations, while Secant Method requires five iterations. From these three methods, Secant Method requires the fewest number of iterations, Regula Falsi Method requires a greater number of iterations than the Secant Method but less than the Bisection Method, and Bisection Method requires the highest number of iterations.
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