SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Plenary Lecture


Computing Operator Determinants and Preconditioning Riemann-Hilbert Problems - A Numerical Analyst's Encounter with Mathematical Physics

F. Bornemann

Abstract
The numerical evaluation of operator determinants, originally born out of an attempt to validate some highly structured differential equations calculations, has become a popular tool in areas of Mathematical and Theoretical Physics dealing with integrable systems; e.g., it was recently used by S. Nishigaki to calculate the 'pion decay constant' of certain QCD-like theories. We review some of this development, tell an amusing story about the numerical evaluation of higher-order derivatives and its relation to a problem in graph theory, and end by showing how all this generalizes to the preconditioning of matrix-valued Riemann-Hilbert problems. Partly joint work with my PhD student Georg Wechslberger (TU München).

Organized by         Universidad de Valladolid     IMUVA