Numerical computation of triangular complex spherical designs with small mesh ratio

被引：0

作者：

Wang, Yu Guang ^{[1
,2
,3
,4
,5
]}

Womersley, Robert S. ^{[1
,2
]}

Wu, Hau-Tieng ^{[6
,7
,8
]}

Yu, Wei-Hsuan ^{[2
,9
]}

机构：

[1] Univ New South Wales, Sch Math & Stat, Sydney, NSW, Australia

[2] Brown Univ, ICERM, Providence, RI USA

[3] Shanghai Jiao Tong Univ, Inst Nat Sci, Shanghai, Peoples R China

[4] Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai, Peoples R China

[5] Shanghai Jiao Tong Univ, LSC, MOE, Shanghai, Peoples R China

[6] Duke Univ, Dept Math, Durham, NC USA

[7] Duke Univ, Dept Stat Sci, Durham, NC USA

[8] Natl Ctr Theoret Sci, Math Div, Taipei, Taiwan

[9] Natl Cent Univ, Dept Math, Taoyuan, Taiwan

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2023年 / 421卷

基金：

澳大利亚研究理事会; 美国国家科学基金会;

关键词：

Complex designs; Numerical integration; Uniform distribution; Quasi-uniform; Spherical designs; UNIFORM DESIGN; POINT SETS; INTEGRATION; SYSTEMS;

D O I：

10.1016/j.cam.2022.114796

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper provides triangular spherical designs for the complex unit sphere Std subset of Cd by exploiting the natural correspondence with the real unit sphere S2d-1 subset of 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.(c) 2022 Published by Elsevier B.V.

引用

页数：15

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