Solving Polynomial Systems Equation by Equation

Andrew J. Sommese; Jan Verschelde; Charles W. Wampler

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Solving Polynomial Systems Equation by Equation

Andrew J. Sommese·Jan Verschelde·Charles W. Wampler

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Abstract

By a numerical continuation method called a diagonal homotopy we can compute the intersection of two positive dimensional solution sets of polynomial systems. This paper proposes to use this diagonal homotopy as the key step in a procedure to intersect general solution sets. Of particular interest is the special case where one of the sets is defined by a single polynomial equation. This leads to an algorithm for finding a numerical representation of the solution set of a system of polynomial equations introducing the equations one-by-one. Preliminary computational experiments show this approach can exploit the special structure of a polynomial system, which improves the performance of the path following algorithms.

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Andrew J. Sommese, Jan Verschelde, Charles W. Wampler. 2005-03-29. Solving Polynomial Systems Equation by Equation. https://arxiv.org/abs/math/0503688

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