Foundations of Computational Mathematics

1. Front Matter

   Pages i-xv

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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

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.

• Algebra
• Algorithmen
• Rechnen in der Mathematik
• algorithms
• calculus
• computational mathematics
• finite field
• numerical analysis
• numerische Mathematik
• scientific computing
• wissenschaftliches Rechnen
• algorithm analysis and problem complexity

• 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

Policies and ethics