On the selection of a transversal to solve nonlinear systems with interval arithmetic

Authors:
Frédéric Goualard;Christophe Jermann
Affiliations:
LINA, FRE CNRS 2729, University of Nantes – France, Nantes cedex 3;LINA, FRE CNRS 2729, University of Nantes – France, Nantes cedex 3
Venue:
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part I
Year:
2006

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Abstract

This paper investigates the impact of the selection of a transversal on the speed of convergence of interval methods based on the nonlinear Gauss-Seidel scheme to solve nonlinear systems of equations. It is shown that, in a marked contrast with the linear case, such a selection does not speed up the computation in the general case; directions for researches on more flexible methods to select projections are then discussed.