Convergence Properties of the Spline Fit

Previous article Next article Convergence Properties of the Spline FitJ. H. Ahlberg and E. N. NilsonJ. H. Ahlberg and E. N. Nilsonhttps://doi.org/10.1137/0111007PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1A I. J. Schoenberg, Contributions to the problem of approximation of equidistant data by analytic functions. Part B. On the problem of osculatory interpolation. A second class of analytic approximation formulae, Quart. Appl. Math., 4 (1946), 112–141 MR0016705 0061.28804 CrossrefISIGoogle Scholar1B I. J. Schoenberg, Contributions to the problem of approximation of equidistant data by analytic functions. Part A. On the problem of smoothing or graduation. A first class of analytic approximation formulae, Quart. Appl. Math., 4 (1946), 45–99 MR0015914 0061.28804 CrossrefISIGoogle Scholar2 I. J. Schoenberg and , Anne Whitney, On Pólya frequence functions. III. The positivity of translation determinants with an application to the interpolation problem by spline curves, Trans. Amer. Math. Soc., 74 (1953), 246–259 MR0053177 ISIGoogle Scholar3 I. J. Schoenberg, Spline functions, convex curves and mechanical quadrature, Bull. Amer. Math. Soc., 64 (1958), 352–357 MR0100746 0085.33701 CrossrefGoogle Scholar4 John C. Holladay, A smoothest curve approximation, Math. Tables Aids Comput, 11 (1957), 233–243 MR0093894 0084.34904 CrossrefGoogle Scholar5 R. S. Johnson, On monosplines of least deviation, Trans. Amer. Math. Soc., 96 (1960), 458–477 MR0122938 0094.03903 CrossrefGoogle Scholar6 F. Landis and , E. N. Nilson, Tables of thermodynamic properties of ionized and dissociated air from 1,500°K to 15,000°K, Report, 1921, Pratt and Whitney Aircraft, 1961 Google Scholar7 J. L. Walsh, , J. H. Ahlberg and , E. N. Nilson, Best approximation properties of the spline fit, J. Math. Mech., 11 (1962), 225–234 MR0137283 0196.48603 ISIGoogle Scholar8 Olga Taussky, A recurring theorem on determinants, Amer. Math. Monthly, 56 (1949), 672–676 MR0032557 0036.01301 CrossrefGoogle Scholar9 J. Todd, Survey of numerical analysis, McGraw-Hill Book Co., Inc., New York, 1962, 227– MR0135221 0101.33601 Google Scholar10 A. M. Ostrowski, Note on bounds for determinants with dominant principal diagonal, Proc. Amer. Math. Soc., 3 (1952), 26–30 MR0052380 0046.01203 CrossrefISIGoogle Scholar11 Thomas Muir, A treatise on the theory of determinants, Revised and enlarged by William H. Metzler, Dover Publications Inc., New York, 1960vii+766 MR0114826 Google Scholar12 F. B. Hildebrand, Introduction to numerical analysis, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1956x+511 MR0075670 0070.12401 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails A High Order Finite Difference Method for the Elastic Wave Equation in Bounded Domains with Nonconforming InterfacesLu Zhang and Siyang WangSIAM Journal on Numerical Analysis, Vol. 60, No. 3 | 27 June 2022AbstractPDF (2241 KB)Matrices with Tunable Infinity-Norm Condition Number and No Need for Pivoting in LU FactorizationMassimiliano Fasi and Nicholas J. HighamSIAM Journal on Matrix Analysis and Applications, Vol. 42, No. 1 | 18 March 2021AbstractPDF (490 KB)Globally Convergent Primal-Dual Active-Set Methods with Inexact Subproblem SolvesSIAM Journal on Optimization, Vol. 26, No. 4 | 26 October 2016AbstractPDF (573 KB)Relative Perturbation Theory for Diagonally Dominant MatricesSIAM Journal on Matrix Analysis and Applications, Vol. 35, No. 4 | 28 October 2014AbstractPDF (389 KB)Monotonicity and Discretization Error EstimatesSIAM Journal on Numerical Analysis, Vol. 27, No. 6 | 14 July 2006AbstractPDF (1701 KB)Natural Cubic and Bicubic Spline InterpolationSIAM Journal on Numerical Analysis, Vol. 10, No. 6 | 14 July 2006AbstractPDF (400 KB)On the Order of Convergence of Natural Cubic Spline InterpolationSIAM Journal on Numerical Analysis, Vol. 5, No. 1 | 14 July 2006AbstractPDF (767 KB)Error Bounds for Interpolation and Differentiation by the Use of Spline FunctionsDon SecrestJournal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis, Vol. 2, No. 3 | 14 July 2006AbstractPDF (599 KB) Volume 11, Issue 1| 1963Journal of the Society for Industrial and Applied Mathematics1-204 History Submitted:26 April 1962Published online:13 July 2006 InformationCopyright © 1963 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0111007Article page range:pp. 95-104ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics