A Tree-based analysis of a family of augmented systems for the computation of singular points
Peter Kunkel · IMA Journal of Numerical Analysis · 1996
The main problem of designing augmented systems or minimally extended systems for the numerical computation of singular points is to find appropriate conditions depending on the type of singular point such that the singular point becomes a regular solution of the inflated system. For the reduced problem, i.e. for the problem after having applied the Lyapunov-Schmidt reduction, this task is solved in singularity theory in the form of recognition theorems. In the present paper we show that there is a constructive transcription rule which allows us to carry over these results to the original problem thus giving an explicit way to design augmented and minimally extended systems.