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dc.contributor.authorMorgan, Alexander P.en_US
dc.contributor.authorSommese, Andrew J.en_US
dc.contributor.authorWatson, Layne T.en_US
dc.date.accessioned2013-06-19T14:36:09Z
dc.date.available2013-06-19T14:36:09Z
dc.date.issued1987
dc.identifierhttp://eprints.cs.vt.edu/archive/00000075/en_US
dc.identifier.urihttp://hdl.handle.net/10919/20243
dc.description.abstractAlthough the theory of polynomial continuation has been established for over a decade (following the work of Garcia, Zangwill, and Drexler), it is difficult to solve polynomial systems using continuation in practice. Divergent paths (solutions at infinity), singular solutions, and extreme scaling of coefficients can create catastrophic numerical problems. Further, the large number of paths that typically arise can be discouraging. In this paper we summarize polynomial-solving homotopy continuation and report on the performance of three standard path-tracking algorithms (as implemented in HOMPACK) in solving three physical problems of varying degrees of difficulty. Our purpose is to provide useful information on solving polynomial systems; including specific guidelines for homotopy construction and parameter settings. The m-homogeneous strategy for constructing polynomial homotopies is outlined, along with more tradition approaches. Computational comparisons are included to illustrate and contrast the major HOMPACK options. The conclusions summarize our numerical experience and discuss areas for future research.en_US
dc.format.mimetypeapplication/pdfen_US
dc.publisherDepartment of Computer Science, Virginia Polytechnic Institute & State Universityen_US
dc.relation.ispartofHistorical Collection(Till Dec 2001)en_US
dc.titleFinding All Isolated Solutions to Polynomial Systems Using Hompacken_US
dc.typeTechnical reporten_US
dc.identifier.trnumberTR-87-28en_US
dc.type.dcmitypeTexten_US
dc.identifier.sourceurlhttp://eprints.cs.vt.edu/archive/00000075/01/TR-87-28.pdf


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