Artigo Revisado por pares

On the Best Approximation of Continuous Functions by Splines

1970; Society for Industrial and Applied Mathematics; Volume: 7; Issue: 3 Linguagem: Inglês

10.1137/0707034

ISSN

1095-7170

Autores

Karl Scherer,

Tópico(s)

Advanced Numerical Analysis Techniques

Resumo

Previous article Next article On the Best Approximation of Continuous Functions by SplinesKarl SchererKarl Schererhttps://doi.org/10.1137/0707034PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] J. H. Ahlberg, , E. N. Nilson and , J. L. Walsh, The theory of splines and their applications, Academic Press, New York, 1967xi+284 MR0239327 0158.15901 Google Scholar[2] Garrett Birkhoff, Local spline approximation by moments, J. Math. Mech., 16 (1967), 987–990 MR0208241 0148.29204 ISIGoogle Scholar[3] Carl de Boor, On uniform approximation by splines, J. Approximation Theory, 1 (1968), 219–235 10.1016/0021-9045(68)90026-9 MR0240519 0193.02502 CrossrefGoogle Scholar[4] Carl de Boor, On the convergence of odd-degree spline interpolation, J. Approximation Theory, 1 (1968), 452–463 10.1016/0021-9045(68)90033-6 MR0237996 0174.09902 CrossrefGoogle Scholar[5] Paul L. Butzer and , Hubert Berens, Semi-groups of operators and approximation, Die Grundlehren der mathematischen Wissenschaften, Band 145, Springer-Verlag New York Inc., New York, 1967xi+318, Berlin-Heidelberg MR0230022 0164.43702 CrossrefGoogle Scholar[6] P. L. Butzer and , K. Scherer, On the fundamental approximation theorems of D. Jackson, S. N. Bernstein and theorems of M. Zamansky and S. B. Stečkin, Aequationes Math., 3 (1969), 170–185 10.1007/BF01817511 MR0264301 0179.09101 CrossrefGoogle Scholar[7] P. L. Butzer and , K. Scherer, Butzer P. L. and , B. Sz.-Nagy, Über die Fundamentalsätze der klassischen Approximationstheorie in abstrakten RäumenAbstract Spaces and Approximation (Proc. Conf., Oberwolfach, 1968), Birkhäuser, Basel, 1969, 113–125, International Series of Numerical Mathematics, vol. 10 MR0262751 0186.11001 CrossrefGoogle Scholar[8] J. Nitsche, Umkehrsätze für Spline-Approximationen, Compositio Math., 21 (1969), 400–416 MR0259436 0199.39302 Google Scholar[9A] 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 Scholar[9B] 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 Scholar[10] L. L. Schumaker, T. N. E. Greville, Approximation by splines, Theory and Applications of Spline Functions (Proceedings of Seminar, Math. Research Center, Univ. of Wisconsin, Madison, Wis., 1968), Academic Press, New York, 1969, 65–85, London MR0239329 0187.32802 Google Scholar[11] S. B. Stečkin, On the order of the best approximations of continuous functions, Izvestiya Akad. Nauk SSSR. Ser. Mat., 15 (1951), 219–242 MR0041959 Google Scholar[12] A. F. Timan, Theory of approximation of functions of a real variable, Translated from the Russian by J. Berry. English translation edited and editorial preface by J. Cossar. International Series of Monographs in Pure and Applied Mathematics, Vol. 34, A Pergamon Press Book. The Macmillan Co., New York, 1963xii+631 MR0192238 Google Scholar[13] M. Zamansky, Classes de saturation de certains procédés d'approximation des séries de Fourier des fonctions continues et applications à quelques problèmes d'approximation, Ann. Sci. École. Norm. Sup. (3), 66 (1949), 19–93 MR0030633 0034.18702 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails References Cross Ref Degree of $L_p$ Approximation by Monotone SplinesC. K. Chui, P. W. Smith, and J. D. Ward17 February 2012 | SIAM Journal on Mathematical Analysis, Vol. 11, No. 3AbstractPDF (1023 KB)Monotone Approximation by SplinesRonald A. De Vore17 February 2012 | SIAM Journal on Mathematical Analysis, Vol. 8, No. 5AbstractPDF (1367 KB)On best error bounds for approximation by piecewise polynomial functionsNumerische Mathematik, Vol. 27, No. 3 Cross Ref On dyadic analysis based on the pointwise dyadic derivativeAnalysis Mathematica, Vol. 1, No. 3 Cross Ref On saturation with splinesJournal of Approximation Theory, Vol. 13, No. 4 Cross Ref A Comparison Approach to Direct Theorems for Polynomial Spline Approximation Cross Ref Characterization of smoothness properties of functions by means of their degree of approximation by splinesJournal of Approximation Theory, Vol. 12, No. 4 Cross Ref Characterization of Generalized Lipschitz Classes by Best Approximation with SplinesKarl Scherer14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 11, No. 2AbstractPDF (1921 KB)Some multidimensional spline approximation methodsJournal of Approximation Theory, Vol. 10, No. 1 Cross Ref A characterization of functions having Zygmund's propertyJournal of Approximation Theory, Vol. 9, No. 4 Cross Ref Saturation and Inverse Theorems for Spline Approximation Cross Ref The degree of approximation by Chebyshevian splines1 January 1973 | Transactions of the American Mathematical Society, Vol. 181, No. 0 Cross Ref A remark on the characterization of Lip 1 by trigonometric best approximationJournal of Approximation Theory, Vol. 5, No. 3 Cross Ref Some results on best possible error bounds for finite element methods and approximation with piecewise polynomial functions27 August 2006 Cross Ref Volume 7, Issue 3| 1970SIAM Journal on Numerical Analysis History Submitted:09 February 1970Published online:14 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0707034Article page range:pp. 418-423ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics

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