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Gaussian Quadrature Error Bound

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Romberg Integration

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institution loginHelpJournalsBooksRegisterJournalsBooksRegisterSign inHelpcloseSign in using your ScienceDirect credentialsUsernamePasswordRemember meForgotten username or password?Sign in via your institutionOpenAthens loginOther institution login Download full text in PDF Article Article + other articles in http://www.sciencedirect.com/science/article/pii/0377042789903269 this issue Loading... Export You have selected 1 citation for export. Help Direct export Save to Mendeley Save to RefWorks Export file Format RIS (for EndNote, ReferenceManager, ProCite) BibTeX Text Content Citation Only Citation and Abstract Export Advanced search Close This document does not have an outline. JavaScript is disabled on your browser. Please enable JavaScript gaussian quadrature to use all the features on this page. Journal of Computational and Applied Mathematics Volume 28, December 1989, Pages 145-154 Error bounds for quadrature formulas near Gaussian quadrature Author links open the overlay panel. Numbers correspond to the affiliation list which can be exposed by using the show more link. Opens overlay Helmut Brass, Opens overlay Klaus-Jürgen gaussian quadrature error Förster Institut für Angewandte Mathematik, Technische Universität Braunschweig, Pockelsstraße 14, D-3300 Braunschweig, FRG Received 8 June 1988, Available online 1 April 2002 Show more doi:10.1016/0377-0427(89)90326-9 Get rights and content Under an Elsevier user license Open Archive AbstractLet Rn be the error functional of a quadrature formula Qn on [−1,1] using n nodes. In this paper we consider estimates of the form |Rn[ƒ]|⩽cm∥ƒ(m)∥, ∥ƒ∥≔sup|x|⩽1|ƒ(x)|, with best possible constant cm, i.e., cm = cm(Rn)≔ sup∥ƒ(m)∥⩽1|Rn[ƒ]|. For the error constants c2n−k(RGn) of the Gaussian quadrature formulas QGn we prove results, which are asymptotically sharp, when n increases and k is fixed. For this latter case, comparing with the corresponding error constants c2n−k(Rn) of every other quadrature formula Qn, we show that the order of magnitude of c2n−k(RGn) cannot be improved in n. In particular, we investigate the question of minimal and maximal values of c2n−k(Rn) in the class of all quadrature formulas Qn having at least algebraic degree of exactness deg(Qn)⩾2n−k−1. Keywords Error constants; Gaussian quadrature; optimal quadrature Download full

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