Abstract
I am delighted to have this opportunity to comment on the work of Steve Smale. Mike Shub was kind enough to give me an advance copy of his excellent paper (Shub [93]), which was very useful for it served as a reminder of the many areas in the theory of computation to which Steve has made major or often seminal contributions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
BLUM, L, SHUB, M., AND SMALE, S. On a Theory of Computation and Complexity Over the Real Numbers: NP-completeness, Recursive Functions and Universal Machines, Bull Amer. Math. Soc. 21 (1989), 1–46
RENEGAR, J. On the Worst Case Arithmetic Complexity of Approximating Zeros of Systems of Polynomials, SIAM J. Comput. 18 (1989), 350–370.
SHUB, M. On the Work of Steve Smale on the Theory of Computation. This volume.
SHUB, M. AND SMALE, S. Computational Complexity, On the Geometry of Polynomials and a Theory of Cost: Part I, Ann. Scient. Ecole. Norm. Sup. 18 (1985), 107–142.
SHUB, M. AND SMALE, S. Computational Complexity, On the Geometry of Polynomials and a Theory of Cost: Part II, SIAM J. Comput. 15 (1986), 145–161.
SMALE, S. The Fundamental Theorem of Algebra and Complexity Theory, Bull. Amer. Math. Soc. 4 (1981), 1–36.
SMALE, S.On the Average Number of Steps in the Simplex Method of Linear Programming, Math. Programming 27 (1983), 242–262.
TRAUB, J.F., WASILKOWSKI, G.W., AND WOUźNIAKOWSKI, H. Information-Based Complexity, Academic Press, Boston, MA, 1988.
TRAUB, J.F. AND WOUźNIAKOWSKI, H. Information-Based Complexity: New Questions for Mathematicians, Math. Intelligencer 13 (1991), 34–43.
WERSCHULZ, A.G.Computational Complexity of Differential and Integral Equations, Oxford University Press, Oxford, 1991.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Traub, J.F. (1993). On Smale’s Work in the Theory of Computation: From Polynomial Zeros to Continuous Complexity. In: Hirsch, M.W., Marsden, J.E., Shub, M. (eds) From Topology to Computation: Proceedings of the Smalefest. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2740-3_31
Download citation
DOI: https://doi.org/10.1007/978-1-4612-2740-3_31
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7648-7
Online ISBN: 978-1-4612-2740-3
eBook Packages: Springer Book Archive