A Priori Estimations of a Global Homotopy Residue Continuation Method

Isabelle Gruais (1) , Nathalie M. M. Cousin-Rittemard (1) , Henk Anton Dijkstra (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Department of Atmospheric Science [Fort Collins]

This work is concerned with the a priori estimations of a global homotopy residue continuation method starting from a disjoint initial guess. Explicit conditions ensuring the quadratic convergence of the underlying Newton-Raphson algorithm are proved.

Mots clés: Continuation methods; Error estimate; Global homotopy; Residue

Domaines: Analyse fonctionnelle [math.FA]

Isabelle Gruais, Nathalie M. M. Cousin-Rittemard, Henk Anton Dijkstra. A Priori Estimations of a Global Homotopy Residue Continuation Method. Numerical Functional Analysis and Optimization, 2005, 26 (4 & 5), pp.507-521. ⟨10.1080/01630560500248306⟩. ⟨hal-00277251⟩