Abstract
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.
Mathematics Subject Classification. Primary: 14Q05; secondary: 14K25.
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Dedicated to Bill Helton on the occasion of his 65th birthday
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Plaumann, D., Sturmfels, B., Vinzant, C. (2012). Computing Linear Matrix Representations of Helton-Vinnikov Curves. In: Dym, H., de Oliveira, M., Putinar, M. (eds) Mathematical Methods in Systems, Optimization, and Control. Operator Theory: Advances and Applications, vol 222. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0411-0_19
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DOI: https://doi.org/10.1007/978-3-0348-0411-0_19
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