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dc.contributor.authorOoura, Takuyaen
dc.contributor.alternative大浦, 拓哉ja
dc.date.accessioned2013-04-04T03:00:01Z-
dc.date.available2013-04-04T03:00:01Z-
dc.date.issued2013-09-
dc.identifier.issn0377-0427-
dc.identifier.urihttp://hdl.handle.net/2433/173114-
dc.description.abstractWe propose an efficient computation method for the infinite integral View the MathML source, whose integrand contains a series of spikes, approximately π apart, growing taller and narrower as x increases. Computing the value of this integral has been a problem since 1984. We herein demonstrate a method using the Hilbert transform for changing this type of singular function into a smooth function and computing the value of the integral to more than one million significant digits using a superconvergent double exponential quadrature method.en
dc.format.mimetypeapplication/pdf-
dc.language.isoeng-
dc.publisherElsevier B.V.en
dc.rights© 2013 Elsevier B.V.en
dc.rightsThis is not the published version. Please cite only the published version.en
dc.rightsこの論文は出版社版でありません。引用の際には出版社版をご確認ご利用ください。ja
dc.subjectNumerical quadratureen
dc.subjectMultiple-precision computationen
dc.subjectDouble exponential quadrature methoden
dc.subjectComputational complexityen
dc.titleFast computation of Goursat’s infinite integral with very high accuracyen
dc.typejournal article-
dc.type.niitypeJournal Article-
dc.identifier.ncidAA00696002-
dc.identifier.jtitleJournal of Computational and Applied Mathematicsen
dc.identifier.volume249-
dc.identifier.spage1-
dc.identifier.epage8-
dc.relation.doi10.1016/j.cam.2013.02.006-
dc.textversionauthor-
dcterms.accessRightsopen access-
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