HOM4PS-2.0: a software package for solving polynomial systems by the polyhedral homotopy continuation method
نویسندگان
چکیده
منابع مشابه
PHoM: Polyhedral Homotopy Continuation Method for Polynomial Systems
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 polyhedrallinear homotopy functions, based on the polyhedral homotopy theory, from input data for a given system of polynomial equations f(x) = 0. The second m...
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Polynomial systems occur in many fields of science and engineering. Polynomial homotopy continuation methods apply symbolic-numeric algorithms to solve polynomial systems. We describe the design and implementation of our web interface and reflect on the application of polynomial homotopy continuation methods to solve polynomial systems in the cloud. Via the graph isomorphism problem we organize...
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HOM4PS-2.0 is a software package in FORTRAN 90 which implements the polyhedral homotopy continuation method for solving polynomial systems. It leads in speed over the existing software packages in the same category by huge margins. This article details the description of the parallel version of HOM4PS2.0, named HOM4PS-2.0para. Excellent scalability in the numerical results shows that the parall...
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We develop an algorithm to find all solutions of a generic system in a family of polynomial systems with parametric coefficients using numerical homotopy continuation and the action of the monodromy group. We argue that the expected number of homotopy paths that this algorithm needs to follow is roughly linear in the number of solutions. We demonstrate that our software implementation is compet...
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A continuation method is presented for computing all isolated roots of a semimixed sparse system of polynomial equations. We introduce mixed subdivisions of Newton polytopes, and we apply them to give a new proof and algorithm for Bernstein's theorem on the expected number of roots. This results in a numerical homotopy with the optimal number of paths to be followed. In this homotopy there is o...
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ژورنال
عنوان ژورنال: Computing
سال: 2008
ISSN: 0010-485X,1436-5057
DOI: 10.1007/s00607-008-0015-6