@article{dc19b6c8a44a419e8f2a9c763902c241,
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}",
note = "Funding Information: The first and second authors acknowledge support from the Australian Research Council under Discovery Project DP180100506 . The third author acknowledges the hospitality of National Center for Theoretical Sciences (NCTS), Taipei, Taiwan during summer, 2019. The last author acknowledges support by Taiwan MOST Grant 107-2115-M-008-010-MY2 . This work was supported by the National Science Foundation under Grant No. DMS-1439786 while the first, second and last authors were in residence at the Institute for Computational and Experimental Research in Mathematics in Providence, RI, during the Point Configurations in Geometry, Physics and Computer Science Program. The authors are also grateful for the helpful discussion with Danylo Radchenko on the proof of the existence of the optimal-order complex spherical designs. The manuscript greatly benefited from the referees comments. This research includes computations using the Linux computational cluster Katana supported by Research Technology Services at UNSW Sydney and a UNSW grant of time on the National Computational Infrastructure (NCI Australia), an NCRIS enabled capability supported by the Australian Government. Funding Information: The first and second authors acknowledge support from the Australian Research Council under Discovery Project DP180100506. The third author acknowledges the hospitality of National Center for Theoretical Sciences (NCTS), Taipei, Taiwan during summer, 2019. The last author acknowledges support by Taiwan MOST Grant 107-2115-M-008-010-MY2. This work was supported by the National Science Foundation under Grant No. DMS-1439786 while the first, second and last authors were in residence at the Institute for Computational and Experimental Research in Mathematics in Providence, RI, during the Point Configurations in Geometry, Physics and Computer Science Program. The authors are also grateful for the helpful discussion with Danylo Radchenko on the proof of the existence of the optimal-order complex spherical designs. The manuscript greatly benefited from the referees comments. This research includes computations using the Linux computational cluster Katana supported by Research Technology Services at UNSW Sydney and a UNSW grant of time on the National Computational Infrastructure (NCI Australia), an NCRIS enabled capability supported by the Australian Government. Publisher Copyright: {\textcopyright} 2022",
year = "2023",
month = mar,
day = "15",
doi = "10.1016/j.cam.2022.114796",
language = "English (US)",
volume = "421",
journal = "Journal of Computational and Applied Mathematics",
issn = "0377-0427",
publisher = "Elsevier",
}