POLSYS GLP: A Parallel General Linear Product Homotopy Code for Solving Polynomial Systems of Equations

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dc.contributor.authorSu, Hai-Junen
dc.contributor.authorMcCarthy, J. Michaelen
dc.contributor.authorSosonkina, Mashaen
dc.contributor.authorWatson, Layne T.en
dc.contributor.departmentComputer Scienceen
dc.date.accessioned2013-06-19T14:35:51Zen
dc.date.available2013-06-19T14:35:51Zen
dc.date.issued2004en
dc.description.abstractGlobally convergent, probability-one homotopy methods have proven to be very effective for finding all the isolated solutions to polynomial systems of equations. After many years of development, homotopy path trackers based on probability-one homotopy methods are reliable and fast. Now, theoretical advances reducing the number of homotopy paths that must be tracked, and in the handling of singular solutions, have made probability-one homotopy methods even more practical. POLSYS GLP consists of Fortran 95 modules for nding all isolated solutions of a complex coefficient polynomial system of equations. The package is intended to be used on a distributed memory multiprocessor in conjunction with HOMPACK90 (Algorithm 777), and makes extensive use of Fortran 95 derived data types and MPI to support a general linear product (GLP) polynomial system structure. GLP structure is intermediate between the partitioned linear product structure used by POLSYS PLP (Algorithm 801) and the BKK-based structure used by PHCPACK. The code requires a GLP structure as input, and although nding the optimal GLP structure is a dicult combinatorial problem, generally physical or engineering intuition about a problem yields a very good GLP structure. POLSYS GLP employs a sophisticated power series end game for handling singular solutions, and provides support for problem denition both at a high level and via hand-crafted code. Dierent GLP structures and their corresponding Bezout numbers can be systematically explored before committing to root finding.en
dc.format.mimetypeapplication/pdfen
dc.identifierhttp://eprints.cs.vt.edu/archive/00000692/en
dc.identifier.sourceurlhttp://eprints.cs.vt.edu/archive/00000692/01/glpTOMS04.pdfen
dc.identifier.trnumberTR-04-15en
dc.identifier.urihttp://hdl.handle.net/10919/20114en
dc.language.isoenen
dc.publisherDepartment of Computer Science, Virginia Polytechnic Institute & State Universityen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectNumerical analysisen
dc.titlePOLSYS GLP: A Parallel General Linear Product Homotopy Code for Solving Polynomial Systems of Equationsen
dc.typeTechnical reporten
dc.type.dcmitypeTexten

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