Publikation: Computing Hermitian determinantal representations of hyperbolic curves
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2015
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International Journal of Algebra and Computation. 2015, 25(8), pp. 1327-1336. ISSN 0218-1967. Available under: doi: 10.1142/S0218196715500435
Zusammenfassung
Every real hyperbolic form in three variables can be realized as the determinant of a linear net of Hermitian matrices containing a positive definite matrix. Such representations are an algebraic certificate for the hyperbolicity of the polynomial and their existence has been proved in several different ways. However, the resulting algorithms for computing determinantal representations are computationally intensive. In this note, we present an algorithm that reduces a large part of the problem to linear algebra and discuss its numerical implementation.
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510 Mathematik
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PLAUMANN, Daniel, Rainer SINN, David E. SPEYER, Cynthia VINZANT, 2015. Computing Hermitian determinantal representations of hyperbolic curves. In: International Journal of Algebra and Computation. 2015, 25(8), pp. 1327-1336. ISSN 0218-1967. Available under: doi: 10.1142/S0218196715500435BibTex
@article{Plaumann2015Compu-31289,
year={2015},
doi={10.1142/S0218196715500435},
title={Computing Hermitian determinantal representations of hyperbolic curves},
number={8},
volume={25},
issn={0218-1967},
journal={International Journal of Algebra and Computation},
pages={1327--1336},
author={Plaumann, Daniel and Sinn, Rainer and Speyer, David E. and Vinzant, Cynthia}
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<dcterms:abstract xml:lang="eng">Every real hyperbolic form in three variables can be realized as the determinant of a linear net of Hermitian matrices containing a positive definite matrix. Such representations are an algebraic certificate for the hyperbolicity of the polynomial and their existence has been proved in several different ways. However, the resulting algorithms for computing determinantal representations are computationally intensive. In this note, we present an algorithm that reduces a large part of the problem to linear algebra and discuss its numerical implementation.</dcterms:abstract>
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