Note on the end game in homotopy zero curve tracking

Authors:
Maria Sosonkina;Layne T. Watson;David E. Stewart
Affiliations:
Virginia Polytechnic Institute & State Univ., Blacksburg;Virginia Polytechnic Institute & State Univ., Blacksburg;Texas A&M Univ., College Station
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
1996

Citing 2
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Abstract

Homotopy algorithms to solve a nonlinear system of equations f(x) = 0 involve tracking the zero curve of a homotopy map p(a, &lgr;, x) from &lgr; = 0 until &lgr; = 1. When the algorithm nears or crosses the hyperplane &lgr; = 1, an “end game” phase is begun to compute the solution x¯ satisfying p(a, &lgr;, x¯) = f(x¯) = 0. This note compares several end game strategies, including the one implemented in the normal flow code FIXPNF in the homotopy software package HOMPACK.