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Analysis of Function Component Complexity for Hypercube Homotopy Algorithms

dc.contributor.authorChakraborty, Amalen
dc.contributor.authorAllison, Donald C. S.en
dc.contributor.authorRibbens, Calvin J.en
dc.contributor.authorWatson, Layne T.en
dc.contributor.departmentComputer Scienceen
dc.date.accessioned2013-06-19T14:36:51Zen
dc.date.available2013-06-19T14:36:51Zen
dc.date.issued1990en
dc.description.abstractProbability-one homotopy algorithms are a class of methods for solving nonlinear systems of equations that globally convergent from an arbitrary starting point with probability one. The essence of these homotopy algorithms is the construction of a homotopy map p-sub a and the subsequent tracking of a smooth curve y in the zero set p-sub a to the -1 (0) of p-sub a. Tracking the zero curve y requires repeated evaluation of the map p-sub a, its n x (v + 1) Jacobian matrix Dp-sub a and numerical linear algebra for calculating the kernel of Dp-sub a. This paper analyzes parallel homotopy algorithms on a hypercube, considering the numerical algebra, several communications topologies and problem decomposition strategies, functions component complexity, problem size, and the effect of different component complexity distributions. These parameters interact in complicated ways, but some general principles can be inferred based on empirical results.en
dc.format.mimetypeapplication/pdfen
dc.identifierhttp://eprints.cs.vt.edu/archive/00000209/en
dc.identifier.sourceurlhttp://eprints.cs.vt.edu/archive/00000209/01/TR-90-27.pdfen
dc.identifier.trnumberTR-90-27en
dc.identifier.urihttp://hdl.handle.net/10919/19593en
dc.language.isoenen
dc.publisherDepartment of Computer Science, Virginia Polytechnic Institute & State Universityen
dc.relation.ispartofHistorical Collection(Till Dec 2001)en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.titleAnalysis of Function Component Complexity for Hypercube Homotopy Algorithmsen
dc.typeTechnical reporten
dc.type.dcmitypeTexten

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