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We extend the key idea behind the generalized Petviashvili method of Ref.\cite{gP} by proposing a novel technique based on a similar idea. Thistechnique systematically eliminates from the iteratively obtained solution amode that is "responsible" either for the divergence or the slow convergence ofthe iterations. We demonstrate, theoretically and with examples, that this modeelimination technique can be used both to obtain some nonfundamental solitarywaves and to considerably accelerate convergence of various iteration methods.As a collateral result, we compare the linearized iteration operators for thegeneralized Petviashvili method and the well-known imaginary-time evolutionmethod and explain how their different structures account for the differencesin the convergence rates of these two methods.

A mode elimination technique to improve convergence of iteration methods for finding solitary waves