## Foundations of Computational Mathematics: Selected Papers of a Conference Held at Rio de Janeiro, January 1997This 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. |

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### Contents

1 | |

Borwein | 16 |

Vicent Caselles Argentina | 23 |

Recognition in Hierarchical Models | 43 |

Continuity XAlgebras Extended Abstract | 63 |

J Maurice Rojas Roger Temam | 77 |

Cambridge MA 02139 USA Bloomington IN 47405 | 90 |

Residues in the Torus and Toric Varieties | 102 |

Questions on Attractors of 3Manifolds | 231 |

A TrustRegion SLCP Model Algorithm for Nonlinear Programming | 246 |

England | 267 |

Sanjoy K Mitter | 277 |

Solving special polynomial systems by using structured matrices | 287 |

Numerical Integration of Differential Equations | 305 |

CEREMADE Diego Pallara | 326 |

Universite ParisDauphine Dipartimento di Matematica | 346 |

Erik S Van Vleck | 104 |

Extended Grzegorczyk Hierarchy in the BSS Model of Computability | 127 |

Peter J Giblin | 152 |

Deptartment of Mathematics | 167 |

On the Qualitative Properties of Modified Equations | 169 |

O Gonzalez A M Stuart martinezime unicamp | 186 |

On One Computational Scheme Solving the Nonstationary Schrödinger | 190 |

Szemerédis Regularity Lemma for Sparse Graphs | 216 |

Numerical Linear Algebra in Optical Imaging | 362 |

Peter Kirrinnis Department of Electrical Engineering | 364 |

380 | |

David E Stewart Farrokh Vatan | 381 |

FiniteDimensional Feedback Control of a Scalar ReactionDiffusion | 382 |

Rigid body dynamics and measure differential inclusions | 405 |

A Complexity Analysis | 424 |

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Foundations of Computational Mathematics: Selected Papers of a Conference ... Felipe Cucker,Michael Shub No preview available - 1996 |

### Common terms and phrases

3-manifold A&SS algebra analysis apply approximation assume ATPSS boolean circuits bottom-up bounded classical coefficients complexity compute condition number conic convergence Corollary curve Davidson algorithm defined definition denote differential equations dimension eigenvalue eigenvector elements Elimination Theory Euclidean exists factors finite finite fields function geometric given graph Grzegorczyk height idempotent induced input integration invariant irreducible irreducible polynomials level lines Lie group linear machine manifolds Math Mathematics matrix mean curvature methods minimizers mod F modified equation monic polynomial monoid multiplication Newton iteration obtain operations ordinary differential equations pair parameter polynomial systems polynomials of degree preconditioner problem Proof properties Proposition prove random graphs real numbers recursive regularity lemma resp Rödl roots Runge–Kutta methods semi-algebraic set semigroup Smale smooth solution space sparse subset symmetry set tangent Theorem theory variables variation vector vertices well-posed problem zero