Tuesday, July 14

MS26
Computational Differentiation and Verified Methods

10:30 AM-12:30 PM
Room: Sidney Smith 2108

Computational Differentiation allows the accurate and efficient determination of first- and higher order derivatives of functions represented by computer code. However, when the flow control of the code itself depends on certain intermediate values of variables, this paradigm formally breaks down and incorrect results may occur. Important cases are the computational differentiation through ODE- and PDE solvers in order to determine dependencies on initial conditions or parameters.

The speakers will give an overview of the current state of computational differentiation, including experiences with differentiation in ODEs, and review some conventional verified schemes for integration of ODEs, in particular, they will discuss new algorithms that allow the rigorous determination of dependencies on initial conditions for systems of ODEs are studied.

10:30 Current Status and Future Trends in Computational Differentiation

Christian Bischof and Paul Hovland, Argonne National Laboratory

11:00 Moved to CP11, 12:15 PM

Ulrich Kulisch and Rudolf Lohner, University of Karlsruhe, Germany

11:00 An Adaptive Verified Numerical Integration Algorithm for Definite Integrals

Ulrike Storck, University of Karlsruhe, Germany

11:30 Automatic Differentiation or Monte-Carlo Methods: Which is Better for Error Estimation?

Vladik Kreinovich, Scott A. Starks, and Raul Trejo, University of Texas, El Paso

12:00 Verified Computational Differentiation through Numerical Integrators

Martin Berz, Organizer