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Homotopy Methods and Global Convergence

  • Book
  • © 1983

Overview

Editors:
  1. B. Curtis Eaves

    1. Standford University, Stanford, USA

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  2. Floyd J. Gould

    1. University of Chicago, Chicago, USA

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  3. Heinz-Otto Peitgen

    1. University of Bremen, Bremen, Federal Republic of Germany

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  4. Michael J. Todd

    1. Cornell University, Ithaca, USA

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Part of the book series: Nato Conference Series (NATOCS, volume 13)

Part of the book sub series: II Systems Science (SYSC)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-viii
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  2. Piecewise Smooth Homotopies

    • J. C. Alexander, T.-Y. Li, J. A. Yorke
    Pages 1-14

  3. Global Convergence Rates of Piecewise-Linear Continuation Methods: A Probabilistic Approach

    • J. C. Alexander, E. V. Slud
    Pages 15-30

  4. Relationships Between Deflation and Global Methods in the Problem of Approximating Additional Zeros of a System of Nonlinear Equations

    • E. L. Allgower, K. Georg
    Pages 31-42

  5. Smooth Homotopies for Finding Zeros of Entire Functions

    • Jack Carr, John Mallet-Paret
    Pages 43-62

  6. Where Solving for Stationary Points by LCPs is Mixing Newton Iterates

    • B. Curtis Eaves
    Pages 63-77

  7. On the Equivalence of the Linear Complementarity Problem and a System of Piecewise Linear Equations: Part II

    • B. C. Eaves, C. E. Lemke
    Pages 79-90

  8. Relations Between PL Maps, Complementary Cones, and Degree in Linear Complementarity Problems

    • C. B. Garcia, F. J. Gould, T. R. Turnbull
    Pages 91-144

  9. A Note on Stepsize Control for Numerical Curve Following

    • K. Georg
    Pages 145-154

  10. On a Class of Linear Complementarity Problems of Variable Degree

    • Roger Howe
    Pages 155-177

  11. Linear Complementarity and the Degree of Mappings

    • Roger Howe, Richard Stone
    Pages 179-223

  12. Sub- and Supersolutions for Nonlinear Operators: Problems of Monotone Type

    • Michael Prüfer
    Pages 225-238

  13. An Efficient Procedure for Traversing Large Pieces in Fixed Point Algorithms

    • R. Saigal
    Pages 239-248

  14. The Application of Fixed Point Methods to Economics

    • John B. Shoven
    Pages 249-261

  15. On a Theory of Cost for Equation Solving

    • Mike Shub, Steven Smale
    Pages 263-265

  16. Algorithms for the Linear Complementarity Problem Which Allow an Arbitrary Starting Point

    • Dolf Talman, Ludo Van der Heyden
    Pages 267-285

  17. Engineering Applications of the Chow-Yorke Algorithm

    • Layne T. Watson
    Pages 287-307

  18. Availability of Computer Codes for Piecewise-Linear and Differentiable Homotopy Methods

    • B. Curtis Eaves, Floyd J. Gould, Heinz-Otto Peitgen, Michael J. Todd
    Pages 309-315

  19. Back Matter

    Pages 317-318
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Keywords

About this book

This Proceedings presents refereed versions of most of the papers presented at the NATO Advanced Research Institute on Homotopy Methods and Global Convergence held in Porto Cervo, Sardinia, June 3-6, 1981. This represents the fourth recent occurrence of an international conference addressing the common theme of fixed point computation. The first such conference, ti tled "Computing Fixed Points with Applications," was held in the Department of Mathematical Sciences at Clemson University, Clemson, South Carolina, June 26-28, 1974 and was sponsored by the Office of Naval Research and the Office of the Army Research Center. The second conference, "Symposium on Analysis and Computation of Fixed Points," was held at the University of Wisconsin, Madison, May 7-8, 1979, under the sponsorship of the National Science Foundation, the U. S. Army, and the Mathematics Research Center of the University of Wisconsin, Madison. The third conference, titled "Symposium on Fixed Point Algorithms and Complementarity," was held at the University of Southampton, Southampton, UK, July 3-5, 1979 and was sponsored by U. N. E. S. C. O. , European Research Office (London), Department of Mathematics (University of Southampton), I. B. M. U. K. , Ltd. , Lloyds Bank, Ltd. , and the Office of Naval Research (London). The Advanced Research Institute held in Sardinia was devoted to the theory and application of modern homotopy methods. The following topics were stressed: Path-Following Techniques; Bottom-Line Applications; Global vs. Classical Methods; and Sta- v vi PREFACE of-the-Art, Perspectives and Potential.

Editors and Affiliations

  • Standford University, Stanford, USA

    B. Curtis Eaves

  • University of Chicago, Chicago, USA

    Floyd J. Gould

  • University of Bremen, Bremen, Federal Republic of Germany

    Heinz-Otto Peitgen

  • Cornell University, Ithaca, USA

    Michael J. Todd

Bibliographic Information

  • Book Title: Homotopy Methods and Global Convergence

  • Editors: B. Curtis Eaves, Floyd J. Gould, Heinz-Otto Peitgen, Michael J. Todd

  • Series Title: Nato Conference Series

  • DOI: https://doi.org/10.1007/978-1-4613-3572-6

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Plenum Press, New York 1983

  • Hardcover ISBN: 978-0-306-41127-4Due: 01 March 1983

  • Softcover ISBN: 978-1-4613-3574-0Published: 19 October 2011

  • eBook ISBN: 978-1-4613-3572-6Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: VIII, 318

  • Topics: Physics, general

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