Approximate Zeros, Arcs of Zero Finding Algorithms, and Higher Order Methods

概述了三个广泛的研究主题。将它们结合在一起的粘合剂是高阶(大于2阶)的零点搜索算法的研究。所提出的研究目标包括有助于理解零点搜索算法的全局行为，将此类高阶算法应用于两点边值问题，以及开发快速寻找“近似零点”的算法。这项研究可能会对动力系统作为例子的来源产生极大的兴趣。库里教授的方法是开始广泛的计算机实验，使这个项目自然成为计算数学课程的一个组成部分。

Three broad research topics are outlined. The glue which binds them is the investigation of zero finding algorithms of higher order (order greater than 2). The goals of the proposed research includes contributions to the understanding of the global behavior of zero finding algorithms, application of such higher order algorithms to two point boundary value problems, and the development of fast algorithms for finding "approximate zeros". This research is likely to be of great interest in dynamical systems as a source of examples. Professor Curry's approach is to begin extensive computer experimentation, making this project a natural one for inclusion in the Computational Mathematics Program.