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Degree of adaptive approximation


Authors: Ronald A. DeVore and Xiang Ming Yu
Journal: Math. Comp. 55 (1990), 625-635
MSC: Primary 41A25; Secondary 41A10, 41A15
DOI: https://doi.org/10.1090/S0025-5718-1990-1035930-5
MathSciNet review: 1035930
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Abstract: We obtain various estimates for the error in adaptive approximation and also establish a relationship between adaptive approximation and free-knot spline approximation.


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  • [1] C. de Boor, Good approximation by splines with variable knots, Spline Functions and Approximation Theory (A. Meir and A. Sharma, eds.), Birkhäuser, 1973, pp. 57-72. MR 0403169 (53:6982)
  • [2] C. de Boor and J. R. Rice, An adaptive algorithm for multivariate approximation giving optimal convergence rates, J. Approx. Theory 25 (1979), 337-359. MR 535936 (81j:41052)
  • [3] M. Š. Birman and M. Z. Solomjak, Piecewise polynomial approximation of functions of the class $ W_p^\alpha $, Math. USSR-Sb. 2 (1967), 295-317.
  • [4] H. G. Burchard and D. F. Hale, Piecewise polynomial approximation on optimal meshes, J. Approx. Theory 14 (1975), 128-147. MR 0374761 (51:10957)
  • [5] R. A. DeVore, A note on adaptive approximation, Approx. Theory Appl. 3 (1987), 74-78. MR 939183 (90a:41036)
  • [6] -, Degree of nonlinear approximation, in Approximation Theory 4 (C. K. Chui, L. L. Schumaker, and J. D. Ward, eds.), Academic Press, 1990, pp. 175-201. MR 1090991 (92e:41021)
  • [7] R. A. DeVore and V. Popov, Interpolation of Besov spaces, Trans. Amer. Math. Soc. 305 (1988), 397-414. MR 920166 (89h:46044)
  • [8] -, Interpolation spaces and non-linear approximation, Function Spaces and Applications (M. Cwikel, J. Peetre, Y. Sagher, and H. Wallin, eds.), Lecture Notes in Math., vol. 1302, Springer, 1988, pp. 191-205. MR 942252 (89b:46003)
  • [9] R. A. DeVore and R. C. Sharpley, Maximal functions measuring smoothness, Mem. Amer. Math. Soc. No. 293 (1984). MR 727820 (85g:46039)
  • [10] P. P. Petrushev, Direct and converse theorems for spline and rational approximation and Besov spaces, Function Spaces and Applications (M. Cwikel, J. Peetre, Y. Sagher, and H. Wallin, eds.), Lecture Notes in Math., vol. 1302, Springer, 1988, pp. 363-377. MR 942281 (89d:41027)
  • [11] J. R. Rice, Adaptive approximation, J. Approx. Theory 16 (1976), 329-337. MR 0403171 (53:6984)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1990-1035930-5
Keywords: Nonlinear approximation, adaptive methods, error of approximation
Article copyright: © Copyright 1990 American Mathematical Society

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