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Foundations of Computational Mathematics

Selected Papers of a Conference Held at Rio de Janeiro, January 1997

  • Conference proceedings
  • © 1997

Overview

Editors:
  1. Felipe Cucker

    1. Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong
      Departament d’Economia, Universitat Pompeu Fabra, Barcelona, Spain

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  2. Michael Shub

    1. I.B.M. T.J. Watson Center, Yorktown Heights, USA

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Table of contents (36 papers)

  1. Front Matter

    Pages i-xv
    Download chapter PDF

  2. Computing Roadmaps of Semi-algebraic Sets on a Variety (Extended Abstract)

    • Saugata Basu, Richard Pollack, Marie-Françoise Roy
    Pages 1-15

  3. Essentially Smooth Lipschitz Functions: Compositions and Chain Rules

    • Jonathan M. Borwein, Warren B. Moors
    Pages 16-22

  4. Junction Detection and Filtering

    • Vicent Caselles, Bartomeu Coll, Jean-Michel Morel
    Pages 23-42

  5. Recognition in Hierarchical Models

    • Peter Dayan
    Pages 43-62

  6. Continuity ∑—Algebras (Extended Abstract)

    • Wilson R. de Oliveira
    Pages 63-74

  7. Condition Number Analysis for Sparse Polynomial Systems

    • Jean-Pierre Dedieu
    Pages 75-101

  8. Residues in the Torus and Toric Varieties

    • Alicia Dickenstein
    Pages 102-103

  9. Piecewise Smooth Orthonormal Factors for Fundamental Solution Matrices

    • Luca Dieci, Erik S. Van Vleck
    Pages 104-111

  10. Algorithms for computing finite semigroups

    • Véronique Froidure, Jean-Eric Pin
    Pages 112-126

  11. Extended Grzegorczyk Hierarchy in the BSS Model of Computability

    • Jean-Sylvestre Gakwaya
    Pages 127-151

  12. Affine-Invariant Symmetry Sets

    • Peter J. Giblin, Guillermo Sapiro
    Pages 152-168

  13. On the Qualitative Properties of Modified Equations

    • O. Gonzalez, A. M. Stuart
    Pages 169-179

  14. Numerical Methods on (and off) Manifolds

    • Arieh Iserles
    Pages 180-189

  15. On One Computational Scheme Solving the Nonstationary Schrödinger Equation with Polynomial Nonlinearity

    • Kh. T. Kholmurodov, I. V. Puzynin, Yu. S. Smirnov
    Pages 190-192

  16. Newton Iteration Towards a Cluster of Polynomial Zeros

    • Peter Kirrinnis
    Pages 193-215

  17. Szemerédi’s Regularity Lemma for Sparse Graphs

    • Y. Kohayakawa
    Pages 216-230

  18. Questions on Attractors of 3-Manifolds

    • Sóstenes Lins
    Pages 231-245

  19. A Trust-Region SLCP Model Algorithm for Nonlinear Programming

    • José Mario Martínez
    Pages 246-255

  20. On the height used by additives BSS machines

    • Martín Matamala
    Pages 256-266
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Keywords

About this book

This book contains a collection of articles corresponding to some of the talks delivered at the Foundations of Computational Mathematics conference held at IMPA in Rio de Janeiro in January 1997. Some ofthe others are published in the December 1996 issue of the Journal of Complexity. Both of these publications were available and distributed at the meeting. Even in this aspect we hope to have achieved a synthesis of the mathematics and computer science cultures as well as of the disciplines. The reaction to the Park City meeting on Mathematics of Numerical Analy­ sis: Real Number Algorithms which was chaired by Steve Smale and had around 275 participants, was very enthusiastic. At the suggestion of Narendra Karmar­ mar a lunch time meeting of Felipe Cucker, Arieh Iserles, Narendra Karmarkar, Jim Renegar, Mike Shub and Steve Smale decided to try to hold a periodic meeting entitled "Foundations of Computational Mathematics" and to form an organization with the same name whose primary purpose will be to hold the meeting. This is then the first edition of FoCM as such. It has been organized around a small collection of workshops, namely - Systems of algebraic equations and computational algebraic geometry - Homotopy methods and real machines - Information-based complexity - Numerical linear algebra - Approximation and PDEs - Optimization - Differential equations and dynamical systems - Relations to computer science - Vision and related computational tools There were also twelve plenary speakers.

Editors and Affiliations

  • Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong

    Felipe Cucker

  • Departament d’Economia, Universitat Pompeu Fabra, Barcelona, Spain

    Felipe Cucker

  • I.B.M. T.J. Watson Center, Yorktown Heights, USA

    Michael Shub

Bibliographic Information

  • Book Title: Foundations of Computational Mathematics

  • Book Subtitle: Selected Papers of a Conference Held at Rio de Janeiro, January 1997

  • Editors: Felipe Cucker, Michael Shub

  • DOI: https://doi.org/10.1007/978-3-642-60539-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1997

  • Softcover ISBN: 978-3-540-61647-4Published: 17 December 1996

  • eBook ISBN: 978-3-642-60539-0Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XV, 441

  • Number of Illustrations: 11 b/w illustrations

  • Topics: Algebra, Number Theory, Geometry, Algorithm Analysis and Problem Complexity, Topology, Analysis

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