Transcendental Equations for Nonlinear Optimization in Hyperbolic Space
We present a novel application of transcendental equations for nonlinear distance optimization in hyperbolic space. Through asymptotic approximations using Fourier and Taylor series expansions, we obtain approximations for the transcendental equations with non-zero real values on the boundary λ. The...
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MDPI AG
2024-08-01
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| author | Pranav Kulkarni Harmanjot Singh |
| author_facet | Pranav Kulkarni Harmanjot Singh |
| author_sort | Pranav Kulkarni |
| collection | DOAJ |
| description | We present a novel application of transcendental equations for nonlinear distance optimization in hyperbolic space. Through asymptotic approximations using Fourier and Taylor series expansions, we obtain approximations for the transcendental equations with non-zero real values on the boundary λ. The series expansion of the logarithmic form of our equations around two arbitrary points <i>P</i><sub>1</sub> and <i>P</i><sub>2</sub> can be used to find values close to definite coordinates on λ. Applying principles from the Poincaré hyperbolic disk—a non-Euclidean space with constant negative curvature—we construct optimization methods following λ of our transcendental equations. |
| format | Article |
| id | doaj-art-6e5fd5ca0c6e40ff8b7adbe79680d97b |
| institution | OA Journals |
| issn | 2673-4591 |
| language | English |
| publishDate | 2024-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Engineering Proceedings |
| spelling | doaj-art-6e5fd5ca0c6e40ff8b7adbe79680d97b2025-08-20T02:00:33ZengMDPI AGEngineering Proceedings2673-45912024-08-01741110.3390/engproc2024074001Transcendental Equations for Nonlinear Optimization in Hyperbolic SpacePranav Kulkarni0Harmanjot Singh1Vice Provost for Undergraduate Education, Stanford University, Palo Alto, CA 94305, USAIndependent Researcher, Jammu 180011, Jammu and Kashmir, IndiaWe present a novel application of transcendental equations for nonlinear distance optimization in hyperbolic space. Through asymptotic approximations using Fourier and Taylor series expansions, we obtain approximations for the transcendental equations with non-zero real values on the boundary λ. The series expansion of the logarithmic form of our equations around two arbitrary points <i>P</i><sub>1</sub> and <i>P</i><sub>2</sub> can be used to find values close to definite coordinates on λ. Applying principles from the Poincaré hyperbolic disk—a non-Euclidean space with constant negative curvature—we construct optimization methods following λ of our transcendental equations.https://www.mdpi.com/2673-4591/74/1/1nonlinear optimizationhyperbolic spacetranscendental equationsPoincaré hyperbolic diskinverse hyperbolic trigonometry |
| spellingShingle | Pranav Kulkarni Harmanjot Singh Transcendental Equations for Nonlinear Optimization in Hyperbolic Space Engineering Proceedings nonlinear optimization hyperbolic space transcendental equations Poincaré hyperbolic disk inverse hyperbolic trigonometry |
| title | Transcendental Equations for Nonlinear Optimization in Hyperbolic Space |
| title_full | Transcendental Equations for Nonlinear Optimization in Hyperbolic Space |
| title_fullStr | Transcendental Equations for Nonlinear Optimization in Hyperbolic Space |
| title_full_unstemmed | Transcendental Equations for Nonlinear Optimization in Hyperbolic Space |
| title_short | Transcendental Equations for Nonlinear Optimization in Hyperbolic Space |
| title_sort | transcendental equations for nonlinear optimization in hyperbolic space |
| topic | nonlinear optimization hyperbolic space transcendental equations Poincaré hyperbolic disk inverse hyperbolic trigonometry |
| url | https://www.mdpi.com/2673-4591/74/1/1 |
| work_keys_str_mv | AT pranavkulkarni transcendentalequationsfornonlinearoptimizationinhyperbolicspace AT harmanjotsingh transcendentalequationsfornonlinearoptimizationinhyperbolicspace |