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Tr. Mat. Inst. Steklova, 2010, Volume 269, Pages 254–264 (Mi tm2902)  

Greedy approximation of characteristic functions

V. N. Temlyakov

University of South Carolina, Columbia, SC, USA

Abstract: We discuss the problem of sparse representation of domains in $\mathbb R^d$. We demonstrate how the recently developed general theory of greedy approximation in Banach spaces can be used in this problem. The use of greedy approximation has two important advantages: (1) it works for an arbitrary dictionary of sets used for sparse representation and (2) the method of approximation does not depend on smoothness properties of the domains and automatically provides a near optimal rate of approximation for domains with different smoothness properties. We also give some lower estimates of the approximation error and discuss a specific greedy algorithm for approximation of convex domains in $\mathbb R^2$.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2010, 269, 247–258

Bibliographic databases:

UDC: 517.518.8
Received in November 2009
Language:

Citation: V. N. Temlyakov, “Greedy approximation of characteristic functions”, Function theory and differential equations, Collected papers. Dedicated to Academician Sergei Mikhailovich Nikol'skii on the occasion of his 105th birthday, Tr. Mat. Inst. Steklova, 269, MAIK Nauka/Interperiodica, Moscow, 2010, 254–264; Proc. Steklov Inst. Math., 269 (2010), 247–258

Citation in format AMSBIB
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\paper Greedy approximation of characteristic functions
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\bookinfo Collected papers. Dedicated to Academician Sergei Mikhailovich Nikol'skii on the occasion of his 105th birthday
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\vol 269
\pages 254--264
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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