Numerical Schubert calculus

Details Numerical Schubert calculus Numerical Schubert calculus

1997-06-10

arxiv.org/abs/alg-geom/9706004v1

J. Symb. Comp., 26 (1998), 767-788.

Mathematics

Algebraic Geometry

24 pages, LaTeX 2e with 2 figures, used epsf.sty

Scientific paper

We develop numerical homotopy algorithms for solving systems of polynomial equations arising from the classical Schubert calculus. These homotopies are optimal in that generically no paths diverge. For problems defined by hypersurface Schubert conditions we give two algorithms based on extrinsic deformations of the Grassmannian: one is derived from a Gr\"obner basis for the Pl\"ucker ideal of the Grassmannian and the other from a SAGBI basis for its projective coordinate ring. The more general case of special Schubert conditions is solved by delicate intrinsic deformations, called Pieri homotopies, which first arose in the study of enumerative geometry over the real numbers. Computational results are presented and applications to control theory are discussed.

Affiliated with

Also associated with

No associations

Rating

Numerical Schubert calculus does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Numerical Schubert calculus, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Numerical Schubert calculus will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-695425