Degree of adaptive approximation

DeVore, Ronald A.; Yu, Xiang Ming

doi:10.1090/S0025-5718-1990-1035930-5

Degree of adaptive approximation
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by Ronald A. DeVore and Xiang Ming Yu PDF

Math. Comp. 55 (1990), 625-635 Request permission

Abstract:

We obtain various estimates for the error in adaptive approximation and also establish a relationship between adaptive approximation and free-knot spline approximation.

References

Carl de Boor, Good approximation by splines with variable knots, Spline functions and approximation theory (Proc. Sympos., Univ. Alberta, Edmonton, Alta., 1972) Internat. Ser. Numer. Math., Vol. 21, Birkhäuser, Basel, 1973, pp. 57–72. MR 0403169
Carl de Boor and John R. Rice, An adaptive algorithm for multivariate approximation giving optimal convergence rates, J. Approx. Theory 25 (1979), no. 4, 337–359. MR 535936, DOI 10.1016/0021-9045(79)90021-2

Piecewise polynomial approximation of functions of the class

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H. G. Burchard and D. F. Hale, Piecewise polynomial approximation on optimal meshes, J. Approximation Theory 14 (1975), no. 2, 128–147. MR 374761, DOI 10.1016/0021-9045(75)90084-2
R. A. DeVore, A note on adaptive approximation, Proceedings of China-U.S. Joint Conference on Approximation Theory (Hangzhou, 1985), 1987, pp. 74–78. MR 939183
Ronald A. DeVore, Degree of nonlinear approximation, Approximation theory VI, Vol. I (College Station, TX, 1989) Academic Press, Boston, MA, 1989, pp. 175–201. MR 1090991
Ronald A. DeVore and Vasil A. Popov, Interpolation of Besov spaces, Trans. Amer. Math. Soc. 305 (1988), no. 1, 397–414. MR 920166, DOI 10.1090/S0002-9947-1988-0920166-3
M. Cwikel, J. Peetre, Y. Sagher, and H. Wallin (eds.), Function spaces and applications, Lecture Notes in Mathematics, vol. 1302, Springer-Verlag, Berlin, 1988. MR 942252, DOI 10.1007/BFb0078857
Ronald A. DeVore and Robert C. Sharpley, Maximal functions measuring smoothness, Mem. Amer. Math. Soc. 47 (1984), no. 293, viii+115. MR 727820, DOI 10.1090/memo/0293
Pencho P. Petrushev, Direct and converse theorems for spline and rational approximation and Besov spaces, Function spaces and applications (Lund, 1986) Lecture Notes in Math., vol. 1302, Springer, Berlin, 1988, pp. 363–377. MR 942281, DOI 10.1007/BFb0078887
John R. Rice, Adaptive approximation, J. Approximation Theory 16 (1976), no. 4, 329–337. MR 403171, DOI 10.1016/0021-9045(79)90021-2