Section: New Results

Complexity of the uncoupling of linear functional systems

Uncoupling algorithms transform a linear differential system of first order into one or several scalar differential equations. We examined in [9] two approaches to uncoupling: the cyclic-vector method (CVM) and the Danilevski-Barkatou-Zürcher algorithm (DBZ). We gave tight size bounds on the scalar equations produced by CVM, and designed a fast variant of CVM whose complexity is quasi-optimal with respect to the output size. We exhibited a strong structural link between CVM and DBZ enabling to show that, in the generic case, DBZ has polynomial complexity and that it produces a single equation, strongly related to the output of CVM. We proved that algorithm CVM is faster than DBZ by almost two orders of magnitude, and provided experimental results that validate the theoretical complexity analyses.