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Abstract:

Numerical homotopy continuation methods for three classes of polynomial systems are presented. For a generic instance of the class, every path leads to a solution and the homotopy is optimal. The counting of the roots mirrors the resolution of a generic system that is used to start up the deformations. Software and applications are discussed.

AMS Subject Classification. 14N10, 14M15, 52A39, 52B20, 52B55, 65H10, 68Q40.

Keywords. polynomial system, numerical algebraic geometry, homotopy, continuation, deformation, path following, dense, sparse, determinantal, Bézout bound, Newton polytope, mixed volume, root count, enumerative geometry, numerical Schubert calculus.

Polynomial Homotopies for dense, sparse
and determinantal Systems

Jan Verschelde

Date: July 11, 1999

-Department of Mathematics
Michigan State University
East Lansing, MI 48824-1027, U.S.A.

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