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

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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.