Nonlinear piecewise polynomial approximation beyond Besov spaces
نویسندگان
چکیده
We study nonlinear n-term approximation in Lp(R) (0 < p <∞) from Courant elements or (discontinuous) piecewise polynomials generated by multilevel nested triangulations of R2 which allow arbitrarily sharp angles. To characterize the rate of approximation we introduce and develop three families of smoothness spaces generated by multilevel nested triangulations. We call them B-spaces because they can be viewed as generalizations of Besov spaces. We use the B-spaces to prove Jackson and Bernstein estimates for n-term piecewise polynomial approximation and consequently characterize the corresponding approximation spaces by interpolation. We also develop methods for n-term piecewise polynomial approximation which capture the rates of the best approximation. 2003 Elsevier Inc. All rights reserved.
منابع مشابه
Nonlinear piecewise polynomial approximation: Theory and Algorithms
Nonlinear piecewise polynomial approximation: Theory and Algorithms Borislav Karaivanov We study nonlinear n-term approximation in Lp(R) (0 < p < ∞) from Courant elements or (discontinuous) piecewise polynomials generated by multilevel nested triangulations of R which allow arbitrarily sharp angles. To characterize the rate of approximation we introduce and develop three families of smoothness ...
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