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PHoM - A polyhedral homotopy continuation method for polynomial systems

Title
PHoM - A polyhedral homotopy continuation method for polynomial systems
Authors
Gunji T.Kim S.Kojima M.Takeda A.Fujisawa K.Mizutani T.
Ewha Authors
김선영
SCOPUS Author ID
김선영scopus
Issue Date
2004
Journal Title
Computing (Vienna/New York)
ISSN
0010-485XJCR Link
Citation
vol. 73, no. 1, pp. 57 - 77
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
PHoM is a software package in C++ for finding all isolated solutions of polynomial systems using a polyhedral homotopy continuation method. Among three modules constituting the package, the first module StartSystem constructs a family of polyhedral-linear homotopy functions, based on the polyhedral homotopy theory, from input data for a given system of polynomial equations f(x) = 0. The second module CMPSc traces the solution curves of the homotopy equations to compute all isolated solutions of f(x) = 0. The third module Verify checks whether all isolated solutions of f(x) = 0 have been approximated correctly. We describe numerical methods used in each module and the usage of the package. Numerical results to demonstrate the performance of PHoM include some large polynomial systems that have not been solved previously.
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자연과학대학 > 수학전공 > Journal papers
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