Properties of Minimal Integration Rules

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Previous article Next article Properties of Minimal Integration RulesNira RichterNira Richterhttps://doi.org/10.1137/0707003PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. E. Barnhill and , J. A. Wixom, Quadratures with remainders of minimum norm. I, Math. Comp., 21 (1967), 66–75 MR0223089 0147.14103 CrossrefISIGoogle Scholar[2] R. E. Barnhill and , J. A. Wixom, Quadratures with remainders of minimum norm. II, Math. Comp., 21 (1967), 382–387 MR0223090 0155.21703 CrossrefISIGoogle Scholar[3] Philip Davis, Errors of numerical approximation for analytic functions, J. Rational Mech. Anal., 2 (1953), 303–313 MR0054348 0050.13005 ISIGoogle Scholar[4] Philip J. Davis, Interpolation and approximation, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1963xiv+393 MR0157156 0111.06003 Google Scholar[5] Ulrich Eckhardt, Einige Eigenschaften Wilfscher Quadraturformeln, Numer. Math., 12 (1968), 1–7 10.1007/BF02170990 MR0256561 0165.51002 CrossrefISIGoogle Scholar[6] Philip Rabinowitz and , Nira Richter, New error coefficients for estimating quadrature errors for analytic functions, Math. Comp., 24 (1970), 561–570 MR0275675 0217.52402 CrossrefISIGoogle Scholar[7] R. A. Valentin, Masters Thesis, Applications of functional analysis to optimal numerical approximation for analytic functions, Doctoral thesis, Division of Applied Mathematics, Brown University, Providence, 1965 Google Scholar[8] Herbert S. Wilf, Exactness conditions in numerical quadrature, Numer. Math., 6 (1964), 315–319 10.1007/BF01386079 MR0179941 0123.12203 CrossrefGoogle Scholar[9] Hiroki Yanagihara, A new method of numerical integration of Gaussian type, Bull. Fukuoka Gakugei Univ. III, 6 (1956), 19–25 MR0148221 0075.12803 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Worst-case optimal approximation with increasingly flat Gaussian kernelsAdvances in Computational Mathematics, Vol. 46, No. 2 | 6 March 2020 Cross Ref On the positivity and magnitudes of Bayesian quadrature weightsStatistics and Computing, Vol. 29, No. 6 | 4 October 2019 Cross Ref Reproducing kernel Hilbert spaces and extremal problems for scattering of particles with arbitrary spinsInternational Journal of Theoretical Physics, Vol. 24, No. 12 | 1 Dec 1985 Cross Ref Reproducing kernel Hilbert spaces and optimal state description of hadron-hadron scatteringInternational Journal of Theoretical Physics, Vol. 24, No. 4 | 1 Apr 1985 Cross Ref The determination of nodes and weights in wilf quadrature formulasAbhandlungen aus dem Mathematischen Seminar der Universität Hamburg, Vol. 48, No. 1 | 1 Apr 1979 Cross Ref Eine Familie interpolatorischer Quadraturformeln mit ableitungsfreien FehlerschrankenNumerische Mathematik, Vol. 28, No. 1 | 1 Mar 1977 Cross Ref Optimale Approximation linearer Funktionale auf periodischen FunktionenNumerische Mathematik, Vol. 22, No. 3 | 1 Jun 1974 Cross Ref Properties of Minimal Integration Rules. IINira Richter-DynSIAM Journal on Numerical Analysis, Vol. 8, No. 3 | 14 July 2006AbstractPDF (910 KB)Minimal Interpolation and Approximation in Hilbert SpacesNira Richter-DynSIAM Journal on Numerical Analysis, Vol. 8, No. 3 | 14 July 2006AbstractPDF (1158 KB)Minimal quadratures for functions of low-order continuityMathematics of Computation, Vol. 25, No. 116 | 1 January 1971 Cross Ref Some polynomials for complex quadratureMathematics of Computation, Vol. 25, No. 116 | 1 January 1971 Cross Ref Asymptotic properties of minimal integration rulesMathematics of Computation, Vol. 24, No. 111 | 1 January 1970 Cross Ref Chebyshev-type integration rules of minimum normMathematics of Computation, Vol. 24, No. 112 | 1 January 1970 Cross Ref Volume 7, Issue 1| 1970SIAM Journal on Numerical Analysis1-198 History Submitted:07 March 1969Published online:14 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0707003Article page range:pp. 67-79ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics