Please use this identifier to cite or link to this item:
http://hdl.handle.net/10397/78233
DC Field | Value | Language |
---|---|---|
dc.contributor | Department of Applied Mathematics | en_US |
dc.creator | Zhou, Y | en_US |
dc.creator | Chen, X | en_US |
dc.date.accessioned | 2018-09-28T01:15:53Z | - |
dc.date.available | 2018-09-28T01:15:53Z | - |
dc.identifier.issn | 0025-5718 | en_US |
dc.identifier.uri | http://hdl.handle.net/10397/78233 | - |
dc.language.iso | en | en_US |
dc.publisher | American Mathematical Society | en_US |
dc.rights | First published in Mathematics of Computation 87(314) (2018), published by the American Mathematical Society. © Copyright 2018 American Mathematical Society. | en_US |
dc.rights | This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/ | en_US |
dc.subject | Spherical t-designs | en_US |
dc.subject | Polynomial approximation | en_US |
dc.subject | Interval analysis | en_US |
dc.subject | Numerical integration | en_US |
dc.subject | L(1)-regularization | en_US |
dc.title | Spherical Tε-designs for approximations on the sphere | en_US |
dc.type | Journal/Magazine Article | en_US |
dc.identifier.spage | 2831 | en_US |
dc.identifier.epage | 2855 | en_US |
dc.identifier.volume | 87 | en_US |
dc.identifier.issue | 314 | en_US |
dc.identifier.doi | 10.1090/mcom/3306 | en_US |
dcterms.abstract | A spherical t-design is a set of points on the unit sphere that are nodes of a quadrature rule with positive equal weights that is exact for all spherical polynomials of degree <= t. The existence of a spherical t-design with (t+1)(2) points in a set of interval enclosures on the unit sphere S-2 subset of R-3 for any 0 <= t <= 100 is proved by Chen, Frommer, and Lang (2011). However, how to choose a set of points from the set of interval enclosures to obtain a spherical t-design with (t + 1) 2 points is not given in loc. cit. It is known that (t + 1)(2) is the dimension of the space of spherical polynomials of degree at most t in 3 variables on S-2. In this paper we investigate a new concept of point sets on the sphere named spherical t(epsilon)-design (0 <= epsilon < 1), which are nodes of a positive, but not necessarily equal, weight quadrature rule exact for polynomials of degree <= t. The parameter epsilon is used to control the variation of the weights, while the sum of the weights is equal to the area of the sphere. A spherical t(epsilon)-design is a spherical t-design when epsilon = 0, and a spherical t-design is a spherical t,design for any 0 < epsilon < 1. We show that any point set chosen from the set of interval enclosures (loc. cit.) is a spherical t(epsilon)-design. We then study the worst-case error in a Sobolev space for quadrature rules using spherical t(epsilon)-designs, and investigate a model of polynomial approximation with l(1)-regularization using spherical t(epsilon)-designs. Numerical results illustrate the good performance of spherical t(epsilon)-designs for numerical integration and function approximation on the sphere. | en_US |
dcterms.accessRights | open access | en_US |
dcterms.bibliographicCitation | Mathematics of computation, Nov. 2018, v. 87, no. 314, p. 2831-2855 | en_US |
dcterms.isPartOf | Mathematics of computation | en_US |
dcterms.issued | 2018 | - |
dc.identifier.isi | WOS:000440340300010 | - |
dc.identifier.eissn | 1088-6842 | en_US |
dc.description.validate | 201809 bcrc | en_US |
dc.description.oa | Accepted Manuscript | en_US |
dc.identifier.FolderNumber | AMA-0405 | - |
dc.description.fundingSource | RGC | en_US |
dc.description.pubStatus | Published | en_US |
dc.identifier.OPUS | 27017189 | - |
Appears in Collections: | Journal/Magazine Article |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Chen_Spherical_T∈-Designs_Approximations.pdf | Pre-Published version | 1.57 MB | Adobe PDF | View/Open |
Page views
101
Last Week
0
0
Last month
Citations as of May 5, 2024
Downloads
23
Citations as of May 5, 2024
SCOPUSTM
Citations
6
Citations as of Apr 19, 2024
WEB OF SCIENCETM
Citations
5
Last Week
0
0
Last month
Citations as of May 2, 2024
Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.