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

三个广泛的研究课题进行了概述。 胶水， 结合他们是零发现算法的调查 更高的阶数（阶数大于2）。 拟议的目标 研究包括对理解 零查找算法的全局行为，这种算法的应用 两点边值问题的高阶算法， 快速算法的发展寻找“近似 零”。 这项研究可能会在动力学方面引起极大的兴趣。 系统作为例子的来源。 咖喱教授的方法是 开始广泛的计算机实验，使这个项目 一个自然的一个包含在计算数学 程序.

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.