On Multivariate Adaptive Approximation |
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| Authors: | Y. K. Hu K. A. Kopotun X. M. Yu |
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| Affiliation: | (1) Department of Mathematics and Computer Science, Georgia Southern University, Statesboro, GA 30360, USA, US;(2) Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA, US;(3) Department of Mathematics, Southwest Missouri State University, Springfield, MO 65804, USA, US |
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| Abstract: | Recently, A. Cohen, R. A. DeVore, P. Petrushev, and H. Xu investigated nonlinear approximation in the space BV (R 2 ). They modified the classical adaptive algorithm to solve related extremal problems. In this paper, we further study the modified adaptive approximation and obtain results on some extremal problems related to the spaces V σ,p r (R d ) of functions of ``Bounded Variation" and Besov spaces B α (R d ). November 23, 1998. Date revised: June 25, 1999. Date accepted: September 13, 1999. |
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| Keywords: | . Nonlinear approximation Approximation spaces Adaptive algorithms Piecewise polynomials Splines Besov spaces Degree of approximation Modulus of smoothness K -Functionals. AMS Classification. 41A15 41A17 41A25 41A27 41A46 41A63. |
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