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Previous article Next article $L^2$-Multivariate Approximation TheoryMartin H. SchultzMartin H. Schultzhttps://doi.org/10.1137/0706018PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Shmuel Agmon, Lectures on elliptic boundary value problems, Prepared for publication by B. Frank Jones, Jr. with the assistance of George W. Batten, Jr. Van Nostrand Mathematical Studies, No. 2, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1965v+291 MR0178246 0142.37401 Google Scholar[2] G. Alexits, Konvergenzprobleme der Orthogonalreihen, Verlag der Ungarischen Akademie der Wissenschaften, Budapest, 1960, 307– MR0162091 0097.27702 Google Scholar[3] 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[4] Felix E. Browder, Approximation-solvability of nonlinear functional equations in normed linear spaces, Arch. Rational Mech. Anal., 26 (1967), 33–42 10.1007/BF00283857 MR0220119 0166.12603 CrossrefISIGoogle Scholar[5] A.-P. Calderón, Lebesgue spaces of differentiable functions and distributionsProc. Sympos. Pure Math., Vol. IV, American Mathematical Society, Providence, R.I., 1961, 33–49 MR0143037 0195.41103 CrossrefGoogle Scholar[6] P. G. Ciarlet, , M. H. Schultz and , R. S. Varga, Numerical methods of high-order accuracy for nonlinear boundary value problems. V. Monotone operator theory, Numer. Math., 13 (1969), 51–77 10.1007/BF02165273 MR0250496 0181.18603 CrossrefISIGoogle Scholar[7] Philip J. Davis, Interpolation and approximation, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1963xiv+393 MR0157156 0111.06003 Google Scholar[8] G. Fix, Masters Thesis, Bounds and approximations for eigenvalues of self-adjoins boundary value problems, Doctoral thesis, Harvard University, Cambridge, 1968 Google Scholar[9] K. O. Friedrichs and , H. B. Keller, J. H. Bramble, A finite difference scheme for generalized Neumann problemsNumerical Solution of Partial Differential Equations (Proc. Sympos. Univ. Maryland, 1965), Academic Press, New York, 1966, 1–19 MR0203956 0147.13901 Google Scholar[10] 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[11] G. G. Lorentz, Approximation of functions, Holt, Rinehart and Winston, New York, 1966ix+188 MR0213785 0153.38901 Google Scholar[12] Edward James McShane, Integration, Princeton University Press, Princeton, N. J., 1944 1957viii+394 pp. (Fourth printing 1957) MR0082536 0060.13010 Google Scholar[13] S. G. Mikhlin, Variational methods in mathematical physics, Translated by T. Boddington; editorial introduction by L. I. G. Chambers. A Pergamon Press Book, The Macmillan Co., New York, 1964xxxii+582 MR0172493 0119.19002 Google Scholar[14] Charles B. Morrey, Jr., Multiple integrals in the calculus of variations, Die Grundlehren der mathematischen Wissenschaften, Band 130, Springer-Verlag New York, Inc., New York, 1966ix+506 MR0202511 0142.38701 CrossrefGoogle Scholar[15] M. H. Schultz and , R. S. Varga, L-splines, Numer. Math., 10 (1967), 345–369 10.1007/BF02162033 MR0225068 0183.44402 CrossrefISIGoogle Scholar[16] Martin H. Schultz, $L\sp{\infty }$-multivariate approximation theory, SIAM J. Numer. Anal., 6 (1969), 184–209 10.1137/0706018 MR0251410 0202.15901 ISIGoogle Scholar[17] Lawrence F. Shampine, An inequality of E. Schmidt, Duke Math. J., 33 (1966), 145–150 10.1215/S0012-7094-66-03319-9 MR0186978 0196.48503 CrossrefISIGoogle Scholar[18] Kôsaku Yosida, Functional analysis, Die Grundlehren der Mathematischen Wissenschaften, Band 123, Academic Press Inc., New York, 1965xi+458 MR0180824 0126.11504 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Konvergenzaussagen f�r Kollokationsverfahren bei elliptischen RandwertaufgabenNumerische Mathematik, Vol. 54, No. 6 Cross Ref On multivariate polynomialL 2-approximation to zeroAnalysis Mathematica, Vol. 10, No. 3 Cross Ref Tensor spline approximationLinear Algebra and its Applications, Vol. 34 Cross Ref Collocation at Gauss Points as a Discretization in Optimal ControlG. W. 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Schultz14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 6, No. 3AbstractPDF (792 KB) Volume 6, Issue 2| 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:10.1137/0706018Article page range:pp. 184-209ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics

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