论文标题
求解非线性方程系统的方法的调查，第一部分：扎根方法
Survey of Methods for Solving Systems of Nonlinear Equations, Part I: Root-finding Approaches
论文作者
论文摘要
本文对方法进行了全面的调查，可用于搜索非线性方程系统（SNES）的解决方案。这项调查的目标是通过详细描述和分析能够找到一种或多种SNE解决方案的已知方法来综合该领域中相关文献，并协助有兴趣的读者寻求识别解决方案技术，这些技术非常适合解决各种类别的SNE，这些SNE可能会在真实的世界应用中遇到。 为了实现这些目标，我们提出了一项多部分调查。在第一部分中，我们专注于从根本上寻找解决方案的方法，而无需将其转换为优化问题。在第二部分中，我们将介绍已用于将SNE转换为优化问题的各种转换，并讨论了优化算法，然后可以使用这些算法来搜索解决方案。在第三部分中，我们将对能够搜索SNE解决方案的方法进行强大的定量比较分析。
This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting a thorough description and analysis of the known methods capable of finding one or many solutions to SNEs, and to assist interested readers seeking to identify solution techniques which are well suited for solving the various classes of SNEs which one may encounter in real world applications. To accomplish these objectives, we present a multi-part survey. In part one, we focus on root-finding approaches which can be used to search for solutions to a SNE without transforming it into an optimization problem. In part two, we will introduce the various transformations which have been utilized to transform a SNE into an optimization problem, and we discuss optimization algorithms which can then be used to search for solutions. In part three, we will present a robust quantitative comparative analysis of methods capable of searching for solutions to SNEs.
