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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-08-01
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| Series: | Engineering Proceedings |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2673-4591/74/1/1 |
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| Summary: | 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. |
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| ISSN: | 2673-4591 |