Relaxed resolution of implicit equations

Joris van der Hoeven (1)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

The technique of relaxed power series expansion provides an efficient way to solve equations of the form F=Phi(F), where the unknown F is a vector of power series, and where the solution can be obtained as the limit of the sequence 0,Phi(0),Phi(Phi(0)),.... With respect to other techniques, such as Newton's method, two major advantages are its generality and the fact that it takes advantage of possible sparseness of Phi. In this paper, we extend the relaxed expansion mechanism to more general implicit equations of the form Phi(F)=0.

Mots clés: Implicit equation; relaxed power series; algorithm

Domaines: Logiciel mathématique [cs.MS]; Complexité [cs.CC]; Systèmes dynamiques [math.DS]

Joris van der Hoeven. Relaxed resolution of implicit equations. 2009. ⟨hal-00441977⟩