Computing Hermitian determinantal representations of hyperbolic curves
| Type of Publication: | Journal article |
| Publication status: | Published |
| Author: | Plaumann, Daniel; Sinn, Rainer; Speyer, David E.; Vinzant, Cynthia |
| Year of publication: | 2015 |
| Published in: | International Journal of Algebra and Computation ; 25 (2015), 8. - pp. 1327-1336. - ISSN 0218-1967 |
| DOI (citable link): | https://dx.doi.org/10.1142/S0218196715500435 |
| Summary: |
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.
|
| Subject (DDC): | 510 Mathematics |
| Bibliography of Konstanz: | Yes |
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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. 25(8), pp. 1327-1336. ISSN 0218-1967. Available under: doi: 10.1142/S0218196715500435
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