Numerical construction of spherical t-designs by Barzilai-Borwein method

Congpei An; Yuchen Xiao

doi:10.1016/j.apnum.2019.10.008

Numerical construction of spherical t-designs by Barzilai-Borwein method

Congpei An^*, Yuchen Xiao^*

^*Corresponding author for this work

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

5 Citations (Scopus)

Abstract

A point set X_N on the unit sphere is a spherical t-design is equivalent to the nonnegative quantity A_N, _t+1 vanished. We show that if X_N is a stationary point set of A_N, _t+1and the minimal singular value of basis matrix is positive, then X_N is a spherical t-design. Moreover, the numerical construction of spherical t-designs is valid by using Barzilai-Borwein method. We obtain numerical spherical t-designs with N = (t+2)²points for t+1 up to 127.

Original language	English
Pages (from-to)	295-302
Journal	Applied Numerical Mathematics
Volume	150
Online published	16 Oct 2019
DOIs	https://doi.org/10.1016/j.apnum.2019.10.008
Publication status	Published - Apr 2020

Research Keywords

Spherical t-design
Variational characterization
Barzilai-Borwein method
Singular value

Access Output

10.1016/j.apnum.2019.10.008

Other Access Options

Check CityUHK Library

Permanent Link

Right click to copy link

Cite this

@article{8a2087d060a24bb8b9ad8a8770ae4bee,

title = "Numerical construction of spherical t-designs by Barzilai-Borwein method",

abstract = "A point set XN on the unit sphere is a spherical t-design is equivalent to the nonnegative quantity AN , t+1 vanished. We show that if XN is a stationary point set of AN , t+1 and the minimal singular value of basis matrix is positive, then XN is a spherical t-design. Moreover, the numerical construction of spherical t-designs is valid by using Barzilai-Borwein method. We obtain numerical spherical t-designs with N = (t+2)2 points for t+1 up to 127.",

keywords = "Spherical t-design, Variational characterization, Barzilai-Borwein method, Singular value",

author = "Congpei An and Yuchen Xiao",

year = "2020",

month = apr,

doi = "10.1016/j.apnum.2019.10.008",

language = "English",

volume = "150",

pages = "295--302",

journal = "Applied Numerical Mathematics",

issn = "0168-9274",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Numerical construction of spherical t-designs by Barzilai-Borwein method

AU - An, Congpei

AU - Xiao, Yuchen

PY - 2020/4

Y1 - 2020/4

N2 - A point set XN on the unit sphere is a spherical t-design is equivalent to the nonnegative quantity AN , t+1 vanished. We show that if XN is a stationary point set of AN , t+1 and the minimal singular value of basis matrix is positive, then XN is a spherical t-design. Moreover, the numerical construction of spherical t-designs is valid by using Barzilai-Borwein method. We obtain numerical spherical t-designs with N = (t+2)2 points for t+1 up to 127.

AB - A point set XN on the unit sphere is a spherical t-design is equivalent to the nonnegative quantity AN , t+1 vanished. We show that if XN is a stationary point set of AN , t+1 and the minimal singular value of basis matrix is positive, then XN is a spherical t-design. Moreover, the numerical construction of spherical t-designs is valid by using Barzilai-Borwein method. We obtain numerical spherical t-designs with N = (t+2)2 points for t+1 up to 127.

KW - Spherical t-design

KW - Variational characterization

KW - Barzilai-Borwein method

KW - Singular value

UR - http://www.scopus.com/inward/record.url?scp=85073822396&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85073822396&origin=recordpage

U2 - 10.1016/j.apnum.2019.10.008

DO - 10.1016/j.apnum.2019.10.008

M3 - RGC 21 - Publication in refereed journal

SN - 0168-9274

VL - 150

SP - 295

EP - 302

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

Numerical construction of spherical t-designs by Barzilai-Borwein method

Abstract

Research Keywords

Access Output

Other Access Options

Permanent Link

Other Files and Links

Fingerprint

Cite this