发表机构
Institute for Computer Science and Control (SZTAKI), Corvinus University of Budapest（匈牙利布达佩斯科维努斯大学控制与计算机科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出paxotopy框架，通过多项式逼近、同伦延拓和牛顿迭代结合，求解含非多项式方程的非线性系统的孤立根。
AI 中文摘要
我们关注包含非多项式方程的非线性方程组。基于近几十年来求解多项式系统的显著进展，以及对超越情形特定例子的若干扩展，我们提出了一种寻找孤立根的通用框架。该框架命名为paxotopy，其步骤为：(1)对超越函数进行多项式逼近；(2)通过同伦延拓法求解逼近的多项式系统；(3)将多项式系统的根作为牛顿迭代的起始点，以得到原系统的解。这些步骤结合了局部方法和全局方法的优势。
英文摘要
We focus on systems of nonlinear equations, where some equations are non-polynomial. Building on the remarkable developments in solving polynomial systems during the recent decades, and on a few extensions to specific examples of the transcendental case, a general framework for finding isolated roots is proposed. The name paxotopy is proposed after (1) Polynomial ApproXimation of the transcendental functions, then (2) solving the approximating polynomial system by the homOTOPY continuation method, and finally (3) the roots of the polynomial systems are used as starting points of a Newton's iteration to arrive at the solutions of the original system. These steps combine the advantages of local and global methods.
