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Approximation by smooth multivariate splines. (English) Zbl 0529.41010


MSC:

41A15 Spline approximation
41A25 Rate of convergence, degree of approximation
41A63 Multidimensional problems
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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.
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