Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/6097
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dc.contributorDepartment of Applied Mathematics-
dc.creatorAn, C-
dc.creatorChen, X-
dc.creatorSloan, IH-
dc.creatorWomersley, RS-
dc.date.accessioned2014-12-11T08:24:52Z-
dc.date.available2014-12-11T08:24:52Z-
dc.identifier.issn0036-1429 (print)-
dc.identifier.issn1095-7170 (online)-
dc.identifier.urihttp://hdl.handle.net/10397/6097-
dc.language.isoenen_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.rights© 2010 Society for Industrial and Applied Mathematicsen_US
dc.subjectSpherical designen_US
dc.subjectFundamental systemen_US
dc.subjectMesh normen_US
dc.subjectMaximum determinanten_US
dc.subjectLebesgue constanten_US
dc.subjectNumerical integrationen_US
dc.subjectInterpolationen_US
dc.subjectInterval methoden_US
dc.titleWell conditioned spherical designs for integration and interpolation on the two-sphereen_US
dc.typeJournal/Magazine Articleen_US
dc.identifier.spage2135-
dc.identifier.epage2157-
dc.identifier.volume48-
dc.identifier.issue6-
dc.identifier.doi10.1137/100795140-
dcterms.abstractA set X[sub N] of N points on the unit sphere is a spherical t-design if the average value of any polynomial of degree at most t over X [sub N] is equal to the average value of the polynomial over the sphere. This paper considers the characterization and computation of spherical t-designs on the unit sphere S² ⊂ ℝ³ when N≥(t+1)², the dimension of the space P [sub t] of spherical polynomials of degree at most t. We show how to construct well conditioned spherical designs with N≥(t+1)² points by maximizing the determinant of a matrix while satisfying a system of nonlinear constraints. Interval methods are then used to prove the existence of a true spherical t-design very close to the calculated points and to provide a guaranteed interval containing the determinant. The resulting spherical designs have good geometrical properties (separation and mesh norm). We discuss the usefulness of the points for both equal weight numerical integration and polynomial interpolation on the sphere and give an example.-
dcterms.accessRightsopen accessen_US
dcterms.bibliographicCitationSIAM journal on numerical analysis, 2010, v. 48, no. 6, p. 2135–2157-
dcterms.isPartOfSIAM journal on numerical analysis-
dcterms.issued2010-
dc.identifier.isiWOS:000285551300006-
dc.identifier.scopus2-s2.0-79251473716-
dc.identifier.rosgroupidr53175-
dc.description.ros2010-2011 > Academic research: refereed > Publication in refereed journal-
dc.description.oaVersion of Recorden_US
dc.identifier.FolderNumberOA_IR/PIRAen_US
dc.description.pubStatusPublisheden_US
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