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In this paper a family of fixed point algorithms for the numerical resolutionof some systems of nonlinear equations is designed and analyzed. The familyintroduced here generalizes the Petviashvili method and can be applied to thenumerical generation of traveling waves in some nonlinear dispersive systems.Conditions for the local convergence are derived and numerical comparisonsbetween different elements of the family are carried out.

Petviashvili type methods for traveling wave computations: I. Analysis of convergence