Numerical Procedures for Interpolation by Spline Functions

Previous article Next article Numerical Procedures for Interpolation by Spline FunctionsT. N. E. GrevilleT. N. E. Grevillehttps: //doi. org/10. 1137/0701005PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1 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 Carl de Boor, Best approximation properties of spline functions of odd degree, J. Math. Mech. , 12 (1963), 747–749 MR0154022 0116. 27601 ISIGoogle Scholar3 W. A. Jenkins, Graduation based on a modification of osculatory interpolation, Trans. Actuar. Soc. Amer. , 28 (1927), 198–215 Google Scholar4 T. N. E. Greville and, Hubert Vaughan, Polynomial interpolation in terms of symbolic operators, Soc. Actuar. Trans. , 6 (1954), 413–476 MR0069943 Google Scholar5 I. J. Schoenberg, 1963, Address given at SIAM Conference on Approximation, Gatlinburg, Tennessee, October 24 Google Scholar6 L. A. Liusternik and, V. J. Sobolev, Elements of functional analysis, Russian Monographs and Texts on Advanced Mathematics and Physics, Vol. 5, Hindustan Publishing Corp. , Delhi, 1961x+411, (translated from the Russian) MR0141967 0096. 07802 Google Scholar7 Ivan S. Sokolnikoff, Advaced Calculus, McGraw-Hill Book Co. , New York, 1939x+446 MR0000277 0023. 11703 Google Scholar8 Hubert Vaughan, Some notes on interpolation, J. Inst. Actuar. , 72 (1946), 482–497 MR0019996 0063. 07986 CrossrefGoogle Scholar9 T. N. E. Greville, Subtabulação por minimos quadrados de diferenças finitas, Bol. Inst. Brasil. Atuária, 2 (1946), 7–34 Google Scholar10 Charles A. Spoerl, Difference-equation interpolation, Trans. Actuar. Soc. Amer. , 44 (1943), 289–325 MR0009510 0063. 07156 Google Scholar11 Robert Weinstock, Calculus of variations with applications to physics and engineering, McGraw-Hill Book Company Inc. , New York-Toronto-London, 1952x+326 MR0052702 0049. 19503 Google Scholar12 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 0051. 33606 ISIGoogle Scholar13 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 Scholar14 I. J. Schoenberg, On best approximations of linear operators, Nederl. Akad. Wetensch. Proc. Ser. A 67 = Indag. Math. , 26 (1964), 155–163 MR0161075 0146. 08501 CrossrefGoogle Scholar15 Arthur Sard, Linear approximation, American Mathematical Society, Providence, R. I. , 1963xi+544, (American Mathematical Society Mathematical Surveys, no. 9) MR0158203 0115. 05403 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Discrete Interpolating and Smoothing Spline FunctionsC. S. Duris14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 14, No. 4AbstractPDF (1018 KB) The Effect of Quadrature Errors in the Computation of L² Piecewise Polynomial ApproximationsPaul D. Patent14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 13, No. 3AbstractPDF (1589 KB) A Note on Obtaining Natural Spline Functions by the Abstract Approach of Atteia and LaurentJ. W. Jerome and L. L. Schumaker14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 5, No. 4AbstractPDF (482 KB) Volume 1, Issue 1| 1964Journal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis History Submitted: 20 January 1964Published online: 14 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI: 10. 1137/0701005Article page range: pp. 53-68ISSN (print): 0887-459XISSN (online): 2168-3581Publisher: Society for Industrial and Applied Mathematics