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

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