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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1901.10840 |
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| _version_ | 1866915071531155456 |
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| author | Beltrán, Carlos Ferizović, Damir |
| author_facet | Beltrán, Carlos Ferizović, Damir |
| contents | Using the theory of determinantal point processes we give upper bounds for the Green and Riesz energies for the rotation group SO(3), with Riesz parameter up to 3. The Green function is computed explicitly, and a lower bound for the Green energy is established, enabling comparison of uniform point constructions on SO(3). The variance of rotation matrices sampled by the determinantal point process is estimated, and formulas for the L2 -norm of Gegenbauer polynomials with index 2 are deduced, which might be of independent interest. Also a simple but effective algorithm to sample points in SO(3) is given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_10840 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Approximation to uniform distribution in SO(3) Beltrán, Carlos Ferizović, Damir Mathematical Physics Numerical Analysis Classical Analysis and ODEs 31C12, 31C20, 52A40 Using the theory of determinantal point processes we give upper bounds for the Green and Riesz energies for the rotation group SO(3), with Riesz parameter up to 3. The Green function is computed explicitly, and a lower bound for the Green energy is established, enabling comparison of uniform point constructions on SO(3). The variance of rotation matrices sampled by the determinantal point process is estimated, and formulas for the L2 -norm of Gegenbauer polynomials with index 2 are deduced, which might be of independent interest. Also a simple but effective algorithm to sample points in SO(3) is given. |
| title | Approximation to uniform distribution in SO(3) |
| topic | Mathematical Physics Numerical Analysis Classical Analysis and ODEs 31C12, 31C20, 52A40 |
| url | https://arxiv.org/abs/1901.10840 |