论文标题
找到有效的根系技术
Root finding techniques that work
论文作者
论文摘要
在大多数介绍性的数值分析教科书中，单个非线性方程的处理通常包括一系列通常不起作用或效率低下的通用方法的集合。这些教科书忽略了教导将方法调整为给定问题的重要性，因此也忽略了为实现这一目标的工具。 这里描述了几种通用技术，这些技术将非线性方程的特定结构或特性纳入解决它的方法中。这可能意味着构造专门针对方程式的方法，或者将方程式转换为相同的方法，现有方法非常适合。这些技术在文献中获得的几个案例研究的帮助进行了说明。
In most introductory numerical analysis textbooks, the treatment of a single nonlinear equation often consists of a collection of all-purpose methods that frequently do not work or are inefficient. These textbooks neglect to teach the importance of adapting a method to the given problem, and consequently also neglect to provide the tools to accomplish this. Several general techniques are described here to incorporate the specific structure or properties of a nonlinear equation into a method for solving it. This can mean the construction of a method specifically tailored to the equation, or the transformation of the equation into an equivalent one for which an existing method is well-suited. The techniques are illustrated with the help of several case studies taken from the literature.
