Multiplicity hunting and approximating multiple roots of polynomial systems
M Giusti, Jean-Claude Yakoubsohn · Contemporary mathematics - American Mathematical Society · 2013
The computation of the multiplicity and the approximation of isolated multiple roots of polynomial systems is a difficult problem. In recent years, there has been an increase of activity in this area. Our goal is to translate the theoretical background developed in the last century on the theory of singularities in terms of computation and complexity. This paper presents several different views that are relevant to address the following issues: predict the multiplicity of a root and/or determine the number of roots in a ball, approximate fast a multiple root and give complexity results for such problems. Finally, we propose a new method to determine a regular system, called equivalent but deflated, i.e., admitting the same root as the initial singular one.