Abstract
This chapter consists of those sections of a longer work [5] which formed the basis for much of the author’s talk at the Smalefest. The longer work contains complete proofs and develops much additional material.
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References
Blum, L., Shub, M., 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.
Eaves, B.C., Rothblum, U.G.: A theory on extending algorithms for parametric problems. Math. Oper. Res. 14 (1989), 502–533.
Renegar, J.: On the computational complexity and geometry of the first order theory of the reals: Parts I, II and III. Journal of Symbolic Computation, Vol. 13, pp. 255–352, 1992.
Renegar, J.: On the computational complexity of approximating solutions for real algebraic formulae.SI AM J. Computing, Vol. 21, No. 6, pp. 1008–1025, 1992.
Renegar, J.: Is it possible to know a problem instance is ill-posed?; Some foundations for a general theory of condition numbers. To appear in Journal of Complexity.
Tarski, A.: A Decision Method for Elementary Algebra and Geometry, University of California Press, San Francisco, 1951.
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© 1993 Springer-Verlag New york, Inc.
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Renegar, J. (1993). Ill-Posed Problem Instances. 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_33
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DOI: https://doi.org/10.1007/978-1-4612-2740-3_33
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7648-7
Online ISBN: 978-1-4612-2740-3
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