On the Work of Steve Smale on the Theory of Computation

Michael Shub

Chapter 28 in From Topology to Computation: Proceedings of the Smalefest, 1993, pp 281-301 from Springer

Abstract: Abstract The theory of computation is the newest and longest segment of Steve Smale’s mathematical career. It is still evolving and, thus, it is difficult to evaluate and isolate the more important of Smale’s contributions. I think they will be as important as his contributions to differential topology and dynamical systems. He has firmly grounded himself in the mathematics of practical algorithms, Newton’s method, and the simplex method of linear programming, inventing the tools and methodology for their analysis. With the experience gained, he is laying foundations for the theory of computation which have a unifying effect on the diverse subjects of numerical analysis, theoretical computer science, abstract mathematics, and mathematical logic. I will try to capture some of the points in this long-term project. Of course, the best thing to do is to read Smale’s original papers; I have not done justice to any of them.

Keywords: Turing Machine; Complex Polynomial; Topological Complexity; Differential Topology; Approximate Zero (search for similar items in EconPapers)
Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2740-3_28

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DOI: 10.1007/978-1-4612-2740-3_28

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