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A Note on Obtaining Natural Spline Functions by the Abstract Approach of Atteia and Laurent

1968; Society for Industrial and Applied Mathematics; Volume: 5; Issue: 4 Linguagem: Inglês

10.1137/0705052

1095-7170

Joseph W. Jerome, Larry L. Schumaker,

Advanced Numerical Methods in Computational Mathematics

Previous article Next article A Note on Obtaining Natural Spline Functions by the Abstract Approach of Atteia and LaurentJ. W. Jerome and L. L. SchumakerJ. W. Jerome and L. L. Schumakerhttps://doi.org/10.1137/0705052PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] M. Atteia, Masters Thesis, Etude de certains noyaux et théorie des fonctions "spline" en analyse numerique, Doctoral thesis, University of Grenoble, 1966 Google Scholar[2] H. B. Curry and , I. J. Schoenberg, On Pólya frequency functions. IV. The fundamental spline functions and their limits, J. Analyse Math., 17 (1966), 71–107 MR0218800 0146.08404 CrossrefISIGoogle 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] T. N. E. Greville, Numerical procedures for interpolation by spline functions, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal., 1 (1964), 53–68 MR0221732 0141.33602 LinkGoogle Scholar[5] Samuel Karlin and , Zvi Ziegler, Chebyshevian spline functions, SIAM J. Numer. Anal., 3 (1966), 514–543 10.1137/0703044 MR0216206 0171.31002 LinkGoogle Scholar[6] P. M. Anselone and , P. J. Laurent, A general method for the construction of interpolating or smoothing spline-functions, Numer. Math., 12 (1968), 66–82 10.1007/BF02170998 MR0249904 0197.13501 CrossrefISIGoogle Scholar[7] I. J. Schoenberg, P. L. Butzer, On interpolation by spline functions and its minimal properties, On Approximation Theory (Proceedings of Conference in Oberwolfach, 1963), Birkhäuser, Basel, 1964, 109–129, Internat. Series of Numerical Math., 5 MR0180785 0147.32101 Google Scholar[8] 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 Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails An abstract formulation of variational refinementJournal of Approximation Theory, Vol. 130, No. 2 | 1 Oct 2004 Cross Ref CALCULATION OF THE SMOOTHING SPLINE WITH WEIGHTED ROUGHNESS MEASUREMathematical Models and Methods in Applied Sciences, Vol. 11, No. 01 | 21 November 2011 Cross Ref ReferencesHandbook of Splines | 1 Jan 1999 Cross Ref On Calculating with B-Splines II. IntegrationNumerische Methoden der Approximationstheorie/Numerical Methods of Approximation Theory | 1 Jan 1976 Cross Ref Spline functions as approximate solutions of boundary-value problemsJournal of Optimization Theory and Applications, Vol. 7, No. 3 | 1 Mar 1971 Cross Ref Volume 5, Issue 4| 1968SIAM Journal on Numerical Analysis647-889 History Submitted:30 October 1967Published online:14 July 2006 InformationCopyright © 1968 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0705052Article page range:pp. 657-663ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics