On Multivariate Adaptive Approximation |
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| Authors: | Y K Hu K A Kopotun X M Yu |
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| Institution: | (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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