Combined symbolic and numerical methods for solving equational systems

Abstract

In this paper we discuss systems developed to assist scientists and engineers to solve their problems based on mathematical models using numerical and symbolic methods. Numerical library routines for numerical algorithms and Computer Algebra Systems (CASs) for symbolic computation are both now well established areas. The recent research interest in these areas is oriented towards combining these solvers, rather than on improving the individual solvers. We analyse the state of research in numerical and symbolic solvers as well as the area of these combining methods or coupled (or combined) systems as they are commonly referred to. We evaluate these coupled systems to identify their essential features and various methods of integration. Based on our analysis we then propose a new strategy for integration which can enhance the facilities provided by the existing symbolic and numerical systems.