×

Adaptive approximation by multivariate smooth splines. (English) Zbl 0493.41009


MSC:

41A15 Spline approximation
41A25 Rate of convergence, degree of approximation
41A63 Multidimensional problems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Barnhill, R. E., Representation and approximation of surfaces, (Rice, J. R., Mathematical Software III (1977), Academic Press: Academic Press New York), 68-119
[2] Birman, M. S.; Solomiak, M. Z., Piecewise-polynomial approximations of functions of the classes \(W_p^{α\)
[3] de Boor, C., Splines as linear combinations of \(B\)-splines, (Lorentz, G. G.; Chui, C. K.; Schumaker, L. L., Approximation Theory II (1976), Academic Press: Academic Press New York), 1-47 · Zbl 0343.41011
[4] de Boor, C.; Rice, J. R., An adaptive algorithm for multivariate approximation giving optimal convergence rates, J. Approx. Theory, 25, 337-359 (1979) · Zbl 0411.41008
[5] Dahmen, W., On multivariate \(B\)-splines, SIAM J. Numer. Anal., 17, 179-191 (1980) · Zbl 0425.41015
[6] Dahmen, W., Approximation by linear combinations of multivariate \(B\)-splines, J. Approx. Theory, 31, 299-324 (1981) · Zbl 0487.41012
[7] Dahmen, W., Approximation by smooth multivariate splines on nonuniform grids, (DeVore, R. A.; Scherer, K., Quantitative Approximation (1980), Academic Press: Academic Press New York), 99-114
[8] Dahmen, W.; DeVore, R.; Scherer, K., Multi-dimensional spline-approximation, SIAM J. Numer. Anal., 17, 380-402 (1980) · Zbl 0437.41010
[9] Kuhn, H. W., Some combinatorial lemmas in topology, IBM J. Res. Develop., 45, 518-524 (1960) · Zbl 0109.15603
[10] Micchelli, C. A., A constructive approach to Kergin interpolation in \(R^k\): multivariate \(B\)-splines and Lagrange interpolation, Rocky Mountain J. Math., 10, 485-497 (1980) · Zbl 0456.41003
[11] Micchelli, C. A., On a numerically efficient method for computing multivariate \(B\)-splines, (Proc. Conf. Multivariate Approximation Theory (1979), Birkhäuser: Birkhäuser Basel), 211-248
[12] Rice, J. R., Multivariate piecewise polynomial approximation, (Handscomb, D. C., Multivariate Approximation (1978), Academic Press: Academic Press New York), 261-277
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.