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dc.contributor.authorBarton, Michael
dc.contributor.authorCalo, Victor M.
dc.date.accessioned2015-11-01T11:11:32Z
dc.date.available2015-11-01T11:11:32Z
dc.date.issued2015-10-26
dc.identifier.citationGaussian quadrature for splines via homotopy continuation: Rules for C2 cubic splines 2015 Journal of Computational and Applied Mathematics
dc.identifier.issn03770427
dc.identifier.doi10.1016/j.cam.2015.09.036
dc.identifier.urihttp://hdl.handle.net/10754/581502
dc.description.abstractWe introduce a new concept for generating optimal quadrature rules for splines. To generate an optimal quadrature rule in a given (target) spline space, we build an associated source space with known optimal quadrature and transfer the rule from the source space to the target one, while preserving the number of quadrature points and therefore optimality. The quadrature nodes and weights are, considered as a higher-dimensional point, a zero of a particular system of polynomial equations. As the space is continuously deformed by changing the source knot vector, the quadrature rule gets updated using polynomial homotopy continuation. For example, starting with C1C1 cubic splines with uniform knot sequences, we demonstrate the methodology by deriving the optimal rules for uniform C2C2 cubic spline spaces where the rule was only conjectured to date. We validate our algorithm by showing that the resulting quadrature rule is independent of the path chosen between the target and the source knot vectors as well as the source rule chosen.
dc.language.isoen
dc.publisherElsevier BV
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S0377042715004896
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational and Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational and Applied Mathematics, 24 October 2015. DOI: 10.1016/j.cam.2015.09.036
dc.subjectGaussian quadrature
dc.subjectB-splines
dc.subjectWell-constrained polynomial system
dc.subjectPolynomial homotopy continuation
dc.titleGaussian quadrature for splines via homotopy continuation: Rules for C2 cubic splines
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentEarth Science and Engineering Program
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)
dc.contributor.departmentPhysical Science and Engineering (PSE) Division
dc.identifier.journalJournal of Computational and Applied Mathematics
dc.eprint.versionPost-print
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)
dc.identifier.arxividarXiv:1505.04391
kaust.personBarton, Michael
kaust.personCalo, Victor M.
kaust.personCalo, Victor M.
refterms.dateFOA2017-10-24T00:00:00Z
dc.date.published-online2015-10-26
dc.date.published-print2016-04


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