Overview
As suggested by the name of our group, we have historically had two main research areas: Numerical Integration and Nonlinear Equations. For a more detailed current list of topics, see Research Topics.Numerical integration
Integration is one of the basic operations in analysis and is needed in about all technical computations. In practical situations, many integrations have to be performed numerically because the analytic evaluation is too complicated or even impossible. The research on numerical integration in the department concentrates on the construction of integration formulas with a high degree of accuracy in one or more variables, and the numerical evaluation of integrals with special complications like a strongly oscillatory or singular integrand. The development of software for automatic numerical integration has always been a major goal.
Nonlinear equations
The interest in solving systems of nonlinear equations originated in the work on numerical integration. The construction of integration rules forced us to study systems of polynomial equations. It developed into an independent research area. The research concentrated on methods to find all solutions of systems on nonlinear equations in a given region. This research was supported by the Fund for Scientific Research - Flanders (F.W.O. - Vlaanderen) and the Flemish Institute for the promotion of Scientific-Technological Research in Industry (I.W.T.).
