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Dynamics of Algorithms

November 17-21, 1997

Organizers:

Rafael de la Llave, University of Texas (Chair)

Jens Lorenz, University of New Mexico

Linda Petzold, University of California-Santa Barbara

There are deep connections between the theory of algorithms and dynamical systems theory.

On one hand, the transformations of data effected by an algorithm can be considered as a dynamical system and the techniques of dynamical systems can be used to analyze properties such as global convergence, asymptotic rates, etc., and eventually lead to better numerical algorithms.

On the other hand, computations in dynamical systems present special challenges. For example, the objects to be discretized are geometric objects or have a very strong algebraic component. What is known a priori of the solutions affects the design of algorithms. Suitably designed algorithms may be used as ingredients in rigorous proofs.

Click on the titles to find abstracts and/or links to presentation materials

MONDAY, NOVEMBER 17 | ||
---|---|---|

W. Miller, R. Gulliver, R. de la Llave |
Welcome and Orientation | |

Uri Ascher, University of British Columbia |
DAEs that should not be solved | |

Roswitha März, Humboldt-Universität Berlin |
Dynamics of DAE-Algorithms | |

Marian Mrozek, University of Krakow |
Representable Multivalued Maps as a Topological Bridge between Dynamics and Finite Mathematics | |

TUESDAY, NOVEMBER 18 | ||

Benedict Leimkuhler, University of Kansas |
Symmetry-Preserving Adaptive Integrators for Coulombic Few-Body Problems | |

Debra Lewis, University of California, Santa Cruz |
Conserving algorithms on Lie groups | |

Erik Van Vleck, Colorado School of Mines |
Applications of Orthogonal Integration Techniques | |

Estela Gavosto, University of Kansas |
Complex Analysis Techniques for the Hánon Map | |

John Guckenheimer, Cornell University |
Computation of periodic orbits using automatic differentiation | |

WEDNESDAY, NOVEMBER 19 | ||

Andrew Stuart, Stanford University |
Convergence Proofs for Numerical Software | |

Michael Shub, IBM Watson Research Center |
Multihomogeneous and Gauss-Newton Methods | |

Marek Rychlik, University of Arizona |
Complexity and applications of parametric algorithms of computational algebraic geometry | |

Ricardo Oliva, IMA/Cornell University |
Combinatorics of complex Hénon mappings | |

George Corliss, Marquette University |
Interval "all together" method for parameter identification | |

Baker Kearfott, University of Southwestern Louisiana |
Automatic verification of dynamical systems properties | |

William Schelter, University of Texas |
Net Math, a web-based computational tool | |

Marek Rychlik, University of Arizona |
Computations with Gröbner bases and applications to dynamical systems | |

THURSDAY, NOVEMBER 20 | ||

James A. Yorke, University of Maryland |
How do we find out what a dynamical system is doing? | |

Tim Sauer, George Mason University |
Scaling laws for shadowing time | |

Donald J. Estep, Georgia Inst. of Technology |
Preservation under discretization of invariant rectangles for solutions of reaction-diffusion equations | |

FRIDAY, NOVEMBER 21 | ||

Sebastian Reich, Konrad-Zuse-Zentrum, Berlin |
Numerical Integration of Hamiltonian Systems with a Complex Solution Behavior | |

Ernst Hairer, University of Geneva |
Asymptotic expansions versus backward analysis for numerical integrators | |

Luca Dieci, Georgia Institute of Technology |
Integration of Matrix Equations: Orthonormal Integrators |