On the numerical evaluation of Fredholm determinants

Some significant quantities in mathematics and physics are most naturally expressed as the Fredholm determinant of an integral operator, most notably many of the distribution functions in random matrix theory. Though their numerical values are of interest, there is no systematic numerical treatment of Fredholm determinants to be found in the literature. Instead, the few numerical evaluations that are available rely on eigenfunction expansions of the operator, if expressible in terms of special functions, or on alternative, numerically more straightforwardly accessible analytic expressions, e.g., in terms of Painlev

• Type: Journal
• Year: 2010
• Where: MOC
• Authors: Folkmar Bornemann
• Keywords: Integral Operators, MOC 2010, Numerical Evaluation, Random Matrix Theory, Security Privacy