HOME    »    PROGRAMS/ACTIVITIES    »    Annual Thematic Program
Dynamics of Algorithms
November 17-21, 1997


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

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
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
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
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
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


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1997-1998 Emerging Applications of Dynamical Systems