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Infinite retrogression in the Eaves—Saigal algorithm

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Abstract

For certain functionsf fromR n toR n, the Eaves—Saigal algorithm computes a path inR n × (0, 1] which converges to a zero off. In this case, it is shown that even whenf is of classC ∞ and has a unique zero, the converging path may retrogress infinitely many times.

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References

  1. E. Artin and H. Braun,Introduction to algebraic topology (Charles E. Merrill, Columbus, OH, 1969).

    Google Scholar 

  2. B.C. Eaves, “Computing Kakutani fixed points”,SIAM Journal on Applied Mathematics 21 (1971) 236–244.

    Google Scholar 

  3. B.C. Eaves, “Homotopies for computation of fixed points”,Mathematical Programming 3 (1972) 1–22.

    Google Scholar 

  4. B.C. Eaves, “Properly labeled simplexes”, in: G.B. Dantzig and B.C. Eaves, eds.,Studies in optimization, Vol. 10, MAA Studies in Mathematics (Springer, Berlin, 1974) 71–93.

    Google Scholar 

  5. B.C. Eaves, “A short course in solving equations with PL homotopies”, in: R.W. Cottle and C.E. Lemke, eds.,Nonlinear Programming, Proceedings of the Ninth SIAM-AMS Symposium in Applied Mathematics (SIAM, Philadelphia, PA, 1976).

    Google Scholar 

  6. B.C. Eaves and R. Saigal, “Homotopies for computation of fixed points on unbounded regions”,Mathematical Programming 3 (1972) 225–237.

    Google Scholar 

  7. M. Kojima, “Studies in piecewise-linear approximations of piecewiseC 1 mappings in fixed points and complementarity theory”,Mathematics of Operations Research 3 (1978) 17–36.

    Google Scholar 

  8. J.R. Munkres,Elementary differential topology, Annals of Mathematics Studies, Number 54 (Princeton University Press, Princeton, NJ, 1966).

    Google Scholar 

  9. M. Spivak,Calculus on manifolds (W.A. Benjamin, New York, 1965).

    Google Scholar 

  10. M.J. Todd, “Union jack triangulations”, in: S. Karamardian, ed.,Fixed points: algorithms and applications (Academic Press, New York, 1977).

    Google Scholar 

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Authors and Affiliations

  1. Stanford University, Stanford, CA, USA

    Peter S. Brooks

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  1. Peter S. Brooks
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Additional information

Army Research Office, Durham, Contract No. DAAG-29-78-G-0026; National Science Foundation Grant No. MCS-77-05623.

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Brooks, P.S. Infinite retrogression in the Eaves—Saigal algorithm. Mathematical Programming 19, 313–327 (1980). https://doi.org/10.1007/BF01581651

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  • DOI: https://doi.org/10.1007/BF01581651

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