The technique of relaxed power series expansion provides an efficient way to solve equations of the form , where the unknown is a vector of power series, and where the solution can be obtained as the limit of the sequence . 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 . In this paper, we extend the relaxed expansion mechanism to more general implicit equations of the form .

Keywords: implicit equation, relaxed power series, algorithm

A.M.S. subject classification: 68W25, 42-04, 68W30, 30B10, 33F05, 11Y55

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