Numerical computation of triangular complex spherical designs with small mesh ratio

Yu Guang Wang; Robert S. Womersley; Hau Tieng Wu; Wei Hsuan Yu

doi:10.1016/j.cam.2022.114796

Numerical computation of triangular complex spherical designs with small mesh ratio

Yu Guang Wang, Robert S. Womersley, Hau Tieng Wu, Wei Hsuan Yu

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

This paper provides triangular spherical designs for the complex unit sphere Ω^d⊂ℂ^d by exploiting the natural correspondence with the real unit sphere S^2d−1⊂R^2d. A variational characterization of triangular complex designs is provided, with particular emphasis on numerical computation of efficient triangular complex designs with good geometric properties as measured by their mesh ratio. We give numerical examples of triangular spherical t-designs on complex unit spheres of dimension d=2 to 6.

Original language	English (US)
Article number	114796
Journal	Journal of Computational and Applied Mathematics
Volume	421
DOIs	https://doi.org/10.1016/j.cam.2022.114796
State	Published - Mar 15 2023

Keywords

Complex designs
Numerical integration
Quasi-uniform
Spherical designs
Uniform distribution

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.cam.2022.114796

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title = "Numerical computation of triangular complex spherical designs with small mesh ratio",

abstract = "This paper provides triangular spherical designs for the complex unit sphere Ωd⊂ℂd by exploiting the natural correspondence with the real unit sphere S2d−1⊂R2d. A variational characterization of triangular complex designs is provided, with particular emphasis on numerical computation of efficient triangular complex designs with good geometric properties as measured by their mesh ratio. We give numerical examples of triangular spherical t-designs on complex unit spheres of dimension d=2 to 6.",

keywords = "Complex designs, Numerical integration, Quasi-uniform, Spherical designs, Uniform distribution",

author = "Wang, {Yu Guang} and Womersley, {Robert S.} and Wu, {Hau Tieng} and Yu, {Wei Hsuan}",

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doi = "10.1016/j.cam.2022.114796",

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AU - Wang, Yu Guang

AU - Womersley, Robert S.

AU - Wu, Hau Tieng

AU - Yu, Wei Hsuan

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Y1 - 2023/3/15

N2 - This paper provides triangular spherical designs for the complex unit sphere Ωd⊂ℂd by exploiting the natural correspondence with the real unit sphere S2d−1⊂R2d. A variational characterization of triangular complex designs is provided, with particular emphasis on numerical computation of efficient triangular complex designs with good geometric properties as measured by their mesh ratio. We give numerical examples of triangular spherical t-designs on complex unit spheres of dimension d=2 to 6.

AB - This paper provides triangular spherical designs for the complex unit sphere Ωd⊂ℂd by exploiting the natural correspondence with the real unit sphere S2d−1⊂R2d. A variational characterization of triangular complex designs is provided, with particular emphasis on numerical computation of efficient triangular complex designs with good geometric properties as measured by their mesh ratio. We give numerical examples of triangular spherical t-designs on complex unit spheres of dimension d=2 to 6.

KW - Complex designs

KW - Numerical integration

KW - Quasi-uniform

KW - Spherical designs

KW - Uniform distribution

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JO - Journal of Computational and Applied Mathematics

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Numerical computation of triangular complex spherical designs with small mesh ratio

Abstract

Keywords

ASJC Scopus subject areas

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