Polynomials with Lorentzian Signature, and Computing Permanents via Hyperbolic Programming
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910887094255616 |
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| author | Dey, Papri |
| author_facet | Dey, Papri |
| contents | We study the class of polynomials whose Hessians evaluated at any point of a closed convex cone have Lorentzian signature. This class is a generalization to the remarkable class of Lorentzian polynomials. We prove that hyperbolic polynomials and conic stable polynomials belong to this class, and the set of polynomials with Lorentzian signature is closed. Finally, we develop a method for computing permanents of nonsingular matrices which belong to a class that includes nonsingular $k$-locally singular matrices via hyperbolic programming. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_02759 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Polynomials with Lorentzian Signature, and Computing Permanents via Hyperbolic Programming Dey, Papri Algebraic Geometry Combinatorics 14P99, 05E14, 05E99, 15A15, , 52A20, 90C25 We study the class of polynomials whose Hessians evaluated at any point of a closed convex cone have Lorentzian signature. This class is a generalization to the remarkable class of Lorentzian polynomials. We prove that hyperbolic polynomials and conic stable polynomials belong to this class, and the set of polynomials with Lorentzian signature is closed. Finally, we develop a method for computing permanents of nonsingular matrices which belong to a class that includes nonsingular $k$-locally singular matrices via hyperbolic programming. |
| title | Polynomials with Lorentzian Signature, and Computing Permanents via Hyperbolic Programming |
| topic | Algebraic Geometry Combinatorics 14P99, 05E14, 05E99, 15A15, , 52A20, 90C25 |
| url | https://arxiv.org/abs/2206.02759 |