Computing Linear Matrix Representations of Helton-Vinnikov Curves

Details Computing Linear Matrix Representations of Helton-Vinnikov Curves Computing Linear Matrix Representations of Helton-Vinnikov Curves

2010-11-28

arxiv.org/abs/1011.6057v1

Mathematics

Algebraic Geometry

19 pages, 3 figures

Scientific paper

Helton and Vinnikov showed that every rigidly convex curve in the real plane bounds a spectrahedron. This leads to the computational problem of explicitly producing a symmetric (positive definite) linear determinantal representation for a given curve. We study three approaches to this problem: an algebraic approach via solving polynomial equations, a geometric approach via contact curves, and an analytic approach via theta functions. These are explained, compared, and tested experimentally for low degree instances.

Affiliated with

Also associated with

No associations

Rating

Computing Linear Matrix Representations of Helton-Vinnikov Curves 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 Computing Linear Matrix Representations of Helton-Vinnikov Curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Computing Linear Matrix Representations of Helton-Vinnikov Curves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-321817