Complexity theoretic aspects of continuation methods for the solution of square or underdetermined systems of polynomial equations have been studied by various authors. In this paper we consider overdetermined systems where there are more equations than unknowns.
We take two approaches to the problem. In the first we study Newton's method for an overdetermined system and then apply it to the elements of a path in the space of problems to produce a path of solutions. In the second we study the map from the variety of solutions to the variety of problems and use its structure to lift a path of problems to solutions. We call these second methods predictor-corrector methods.
By: J. P. Dedieu, M. Shub
Published in: RC21109 in 1998
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