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On the Order of Convergence of Natural Cubic Spline Interpolation

1968; Society for Industrial and Applied Mathematics; Volume: 5; Issue: 1 Linguagem: Inglês

10.1137/0705007

1095-7170

Kendall Atkinson,

Numerical Methods and Algorithms

Previous article Next article On the Order of Convergence of Natural Cubic Spline InterpolationKendall E. AtkinsonKendall E. Atkinsonhttps://doi.org/10.1137/0705007PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] J. H. Ahlberg and , E. N. Nilson, Convergence properties of the spline fit, J. Soc. Indust. Appl. Math., 11 (1963), 95–104 10.1137/0111007 MR0152788 0196.48701 LinkISIGoogle Scholar[2] Garrett Birkhoff and , Carl de Boor, Error bounds for spline interpolation, J. Math. Mech., 13 (1964), 827–835 MR0165294 0143.28503 ISIGoogle Scholar[3] Carl de Boor, Best approximation properties of spline functions of odd degree, J. Math. Mech., 12 (1963), 747–749 MR0154022 0116.27601 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] I. J. Schoenberg, Spline interpolation and best quadrature formulae, Bull. Amer. Math. Soc., 70 (1964), 143–148 MR0157157 0136.36202 CrossrefISIGoogle Scholar[6] H. F. Weinberger, Optimal approximation for functions prescribed at equally spaced points, J. Res. Nat. Bur. Standards Sect. B, 65B (1961), 99–104 MR0140194 0168.14901 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Regularization in Reproducing Kernel Hilbert SpacesRegularized System Identification | 14 May 2022 Cross Ref Nonparametric Model Prediction for Intelligent Regulation of Human Cardiorespiratory System to Prescribed Exercise MedicineIEEE Access, Vol. 8 | 1 Jan 2020 Cross Ref Studies of the resonance structure in $$D^{0} \rightarrow K^\mp \pi ^\pm \pi ^\pm \pi ^\mp $$ D 0 → K ∓ π ± π ± π ∓ decaysThe European Physical Journal C, Vol. 78, No. 6 | 2 June 2018 Cross Ref Two cubic spline methods for solving Fredholm integral equationsApplied Mathematics and Computation, Vol. 276 | 1 Mar 2016 Cross Ref A natural spline interpolation and exponential parameterization1 Jan 2016 Cross Ref Rapid detection of new and expanding human settlements in the Limpopo province of South Africa using a spatio-temporal change detection methodInternational Journal of Applied Earth Observation and Geoinformation, Vol. 40 | 1 Aug 2015 Cross Ref Ultrasonic tomographic velocimeter for visualization of axial flow fields in pipesFlow Measurement and Instrumentation, Vol. 41 | 1 Mar 2015 Cross Ref Kernel methods in system identification, machine learning and function estimation: A surveyAutomatica, Vol. 50, No. 3 | 1 Mar 2014 Cross Ref New Trends in Nonparametric Linear System IdentificationModelling Methodology for Physiology and Medicine | 1 Jan 2014 Cross Ref An algorithm to estimate unsteady and quasi-steady pressure fields from velocity field measurementsJournal of Experimental Biology, Vol. 5 | 1 January 2013 Cross Ref A study of the uniform accuracy of univariate thin plate spline interpolationApplied Numerical Mathematics, Vol. 62, No. 12 | 1 Dec 2012 Cross Ref Local Accuracy for Radial Basis Function Interpolation on Finite Uniform GridsJournal of Approximation Theory, Vol. 99, No. 2 | 1 Aug 1999 Cross Ref ReferencesHandbook of Splines | 1 Jan 1999 Cross Ref Studies on extremal problems of spline-approximationUkrainian Mathematical Journal, Vol. 42, No. 1 | 1 Jan 1990 Cross Ref On cubic spline functions that vanish at all knotsAdvances in Mathematics, Vol. 20, No. 1 | 1 Apr 1976 Cross Ref Natural Cubic and Bicubic Spline InterpolationC. A. HallSIAM Journal on Numerical Analysis, Vol. 10, No. 6 | 14 July 2006AbstractPDF (400 KB)Über die Konvergenz von natürlichen interpolierenden SplinesLinear Operators and Approximation / Lineare Operatoren und Approximation | 1 Jan 1972 Cross Ref Application of Besov spaces to spline approximationJournal of Approximation Theory, Vol. 4, No. 3 | 1 Sep 1971 Cross Ref A Note on the Convergence of Interpolatory Cubic SplinesD. KershawSIAM Journal on Numerical Analysis, Vol. 8, No. 1 | 14 July 2006AbstractPDF (546 KB)Saturation bei Spline-Approximation und QuadraturNumerische Mathematik, Vol. 16, No. 2 | 1 Nov 1970 Cross Ref Errors in cubic spline interpolationJournal of Engineering Mathematics, Vol. 3, No. 2 | 1 Apr 1969 Cross Ref Volume 5, Issue 1| 1968SIAM Journal on Numerical Analysis1-197 History Submitted:20 April 1967Published online:14 July 2006 InformationCopyright © 1968 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0705007Article page range:pp. 89-101ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics