发表机构
National Institute of Technology, Kagoshima College; Kyushu University（鹿儿岛工业高等专门学校; 九州大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种修正函数为正且有界的Halley型三阶迭代法，避免奇异性并保持收敛性，数值实验验证其高效稳健，并成功应用于范德瓦尔斯方程。
AI 中文摘要
本文通过修改Halley方法，提出了一种新的单点迭代方法，用于求解非线性方程的简单根。其修正函数在$\mathbb{R}$上为正且有界，并在简单根附近与Halley修正函数的局部展开相匹配。该方法避免了Halley修正函数的奇异性和符号反转，同时保持了至少三阶的局部收敛性。我们还建立了全局收敛的充分条件。数值实验表明，所提方法在广泛的初始猜测范围内实现了高收敛成功率和有利的迭代次数。在Halley修正函数奇点附近的进一步实验证明了所提方法的稳健收敛行为。对范德瓦尔斯方程的应用说明了所提方法的有效性。
英文摘要
In this paper, we propose a new one-point iterative method for finding simple roots of nonlinear equations by modifying Halley's method. Its correction function is positive and bounded on $\mathbb{R}$ and matches the local expansion of Halley's correction function near a simple root. The method avoids the singularity and sign reversal of Halley's correction function while retaining at least third-order local convergence. We also establish sufficient conditions for global convergence. Numerical experiments show that the proposed method achieves high convergence success rates and favorable iteration counts over a wide range of initial guesses. Further experiments near the singularity of Halley's correction function demonstrate robust convergence behavior of the proposed method. An application to the van der Waals equation illustrates the effectiveness of the proposed method.
Comments23 pages
