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 |
