SS15 - Reliable numerical computing and differential equations

link to the session's webpage

One of the key advantages of computer algebra and symbolic computation is the mathematical exactness of all computed results. This session concerns a similar goal of exact mathematical computations for objects of a more analytic nature, through numerical approximations with provable error bounds. One particularly important application concerns the reliable integration of differential equations and the reliable evaluation of special functions. More generally, topics of interest include, but are not limited to:

• Logical foundations of reliable computation.
• Interval and ball arithmetic.
• High performance implementations of reliable algorithms.
• Reliable evaluation of special functions.
• Reliable integration of dynamical systems.
• Reliable homotopy continuation.
• Effective computations with analytic functions.
• Other applications of reliable computation.
• Mathematical software for reliable computations.

We welcome both theoretical and practical contributions as well as applications. The scope is wide and intended to encourage discussions and new collaborations during the conference.

Session organizers

Joris van der Hoeven (CNRS, École polytechnique, France)

Grégoire Lecerf (CNRS, École polytechnique, France)

Talks

Barbara Betti - Proudfoot-Speyer degenerations of scattering equations

Alexandre Guillemot - Braid monodromy computations using certified path tracking

Fabrice Rouillier - Some challenges and applications for continuation methods for solving algebraic systems

Fredrik Johansson - Vector-friendly numbers with n-word precision

Long Qian - Logical Completeness of Differential Equations