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Numerical solution of multivariate polynomial systems by homotopy continuation methods

Published online by Cambridge University Press:  07 November 2008

T. Y. Li
T. Y. Li
Affiliation:
Department of MathematicsMichigan State UniversityEast Lansing, MI 48824–1027USA E-mail: li@math.msu.edu
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Let P(x) = 0 be a system of n polynomial equations in n unknowns. Denoting P = (p1,…, pn), we want to find all isolated solutions of

for x = (x1,…,xn). This problem is very common in many fields of science and engineering, such as formula construction, geometric intersection problems, inverse kinematics, power flow problems with PQ-specified bases, computation of equilibrium states, etc. Elimination theory-based methods, most notably the Buchberger algorithm (Buchberger 1985) for constructing Gröbner bases, are the classical approach to solving (1.1), but their reliance on symbolic manipulation makes those methods seem somewhat unsuitable for all but small problems.

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Research Article
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Acta Numerica , Volume 6 , January 1997 , pp. 399 - 436
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Copyright © Cambridge University Press 1997

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