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arXiv · 1104.2084

Adaptative Step Size Selection for Homotopy Methods to Solve Polynomial Equations

Jean-Pierre Dedieu·Gregorio Malajovich·Michael Shub
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Abstract

Given a C^1 path of systems of homogeneous polynomial equations f_t, t in [a,b] and an approximation x_a to a zero zeta_a of the initial system f_a, we show how to adaptively choose the step size for a Newton based homotopy method so that we approximate the lifted path (f_t,zeta_t) in the space of (problems, solutions) pairs. The total number of Newton iterations is bounded in terms of the length of the lifted path in the condition metric.

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Jean-Pierre Dedieu, Gregorio Malajovich, Michael Shub. 2011-09-02. Adaptative Step Size Selection for Homotopy Methods to Solve Polynomial Equations. https://doi.org/10.1093/imanum%2Fdrs007

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