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$L^2 $-Approximation Theory of Even Order Multivariate Splines

1969; Society for Industrial and Applied Mathematics; Volume: 6; Issue: 3 Linguagem: Inglês

10.1137/0706042

1095-7170

Martin H. Schultz,

Mathematical Approximation and Integration

Previous article Next article $L^2 $-Approximation Theory of Even Order Multivariate SplinesMartin H. SchultzMartin H. Schultzhttps://doi.org/10.1137/0706042PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] G. Birkhoff, , M. H. Schultz and , R. S. Varga, Piecewise Hermite interpolation in one and two variables with applications to partial differential equations, Numer. Math., 11 (1968), 232–256 10.1007/BF02161845 MR0226817 0159.20904 CrossrefISIGoogle Scholar[2] 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[3] Einar Hille, , G. Szegö and , J. D. Tamarkin, On some generalizations of a theorem of A. Markoff, Duke Math. J., 3 (1937), 729–739 10.1215/S0012-7094-37-00361-2 MR1546027 0018.01201 CrossrefGoogle Scholar[4] C. B. Morrey, Multiple Integrals in the Calculus of Variations, Macmillan, New York, 1964 Google Scholar[5] Arthur Sard, Linear approximation, American Mathematical Society, Providence, R.I., 1963xi+544, Mathematical Survey, no. IX MR0158203 0115.05403 CrossrefGoogle Scholar[6] Martin H. Schultz, $L\sp{2}$-multivariate approximation theory, SIAM J. Numer. Anal., 6 (1969), 161–183 10.1137/0706017 MR0251409 LinkISIGoogle Scholar[7] Martin H. Schultz, $L\sp{\infty }$-multivariate approximation theory, SIAM J. Numer. Anal., 6 (1969), 184–209 10.1137/0706018 MR0251410 0202.15901 LinkISIGoogle Scholar[8] M. H. Schultz and , R. S. Varga, L-splines, Numer. Math., 10 (1967), 345–369 10.1007/BF02162033 MR0225068 0183.44402 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails ReferencesHandbook of Splines | 1 Jan 1999 Cross Ref A BIBLIOGRAPHY OF MULTIVARIATE APPROXIMATIONTopics in Multivariate Approximation | 1 Jan 1987 Cross Ref Some projection methods for the eigenvalue problemApplicable Analysis, Vol. 6, No. 1 | 2 May 2007 Cross Ref Stability of the Rayleigh-Ritz procedure for nonlinear two-point boundary value problemsNumerische Mathematik, Vol. 24, No. 1 | 1 Feb 1975 Cross Ref Appendix A A Set of Orthonormal PolynomialsComputer-Oriented Approaches to Pattern Recognition | 1 Jan 1972 Cross Ref On smooth interpolation by continuously connected piecewise polynomialsRendiconti del Circolo Matematico di Palermo, Vol. 20, No. 2-3 | 1 May 1971 Cross Ref Rayleigh–Ritz–Galerkin Methods for Multidimensional ProblemsMartin H. SchultzSIAM Journal on Numerical Analysis, Vol. 6, No. 4 | 14 July 2006AbstractPDF (1349 KB)Approximation Theory of Multivariate Spline Functions in Sobolev SpacesMartin H. SchultzSIAM Journal on Numerical Analysis, Vol. 6, No. 4 | 14 July 2006AbstractPDF (1070 KB) Volume 6, Issue 3| 1969SIAM Journal on Numerical Analysis History Submitted:18 September 1968Published online:14 July 2006 InformationCopyright © 1969 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0706042Article page range:pp. 467-475ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics