de Boor, C.; DeVore, R. Approximation by smooth multivariate splines. (English) Zbl 0529.41010 Trans. Am. Math. Soc. 276, 775-788 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 5 ReviewsCited in 55 Documents MSC: 41A15 Spline approximation 41A25 Rate of convergence, degree of approximation 41A63 Multidimensional problems Keywords:multivariate splines; partitions; smoothness; degree of approximation; multivariate B-splines PDFBibTeX XMLCite \textit{C. de Boor} and \textit{R. DeVore}, Trans. Am. Math. Soc. 276, 775--788 (1983; Zbl 0529.41010) Full Text: DOI References: [1] C. de Boor and G. Fix, Spline approximation by quasi-interpolants, J. Approx. Theory 7 (1973), 19-45. · Zbl 0279.41008 [2] Carl de Boor and Klaus Höllig, Recurrence relations for multivariate \?-splines, Proc. Amer. Math. Soc. 85 (1982), no. 3, 397 – 400. · Zbl 0506.41008 [3] -, \( B\)-splines from parallelepipeds, MRC TSR #2320, 1982. [4] Wolfgang Dahmen, On multivariate \?-splines, SIAM J. Numer. Anal. 17 (1980), no. 2, 179 – 191. · Zbl 0425.41015 · doi:10.1137/0717017 [5] W. Dahmen, R. DeVore, and K. Scherer, Multidimensional spline approximation, SIAM J. Numer. Anal. 17 (1980), no. 3, 380 – 402. · Zbl 0437.41010 · doi:10.1137/0717033 [6] P. O. Frederickson, Generalized triangular splines, Math. Report 7-71, Lakehead University, 1971. [7] P. O. Frederickson, Quasi-interpolation, extrapolation, and approximation on the plane, Proceedings of the Manitoba Conference on Numerical Mathematics (Univ. Manitoba, Winnipeg, Man., 1971) Dept. Comput. Sci., Univ. Manitoba, Winnipeg, Man., 1971, pp. 159 – 167. · Zbl 0263.65006 [8] Charles A. Micchelli, On a numerically efficient method for computing multivariate \?-splines, Multivariate approximation theory (Proc. Conf., Math. Res. Inst., Oberwolfach, 1979) Internat. Ser. Numer. Math., vol. 51, Birkhäuser, Basel-Boston, Mass., 1979, pp. 211 – 248. · Zbl 0422.41008 [9] P. Sablonniere, De l’existence de spline à support borné sur une triangulation équilatérale du plan, Publication ANO-39, U.E.R. d’I.E.E.A.-Informatique, Université de Lille I, February 1981. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.