The best m-term approximation and greedy algorithms |
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Authors: | Temlyakov VN |
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Institution: | (1) Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA |
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Abstract: | Two theorems on nonlinear
‐term approximation in
, are proved in this paper. The first one (theorem 2.1) says that if a basis
is
‐equivalent to the Haar basis then a near best
>‐term approximation to any
can be realized by the following simple greedy type algorithm. Take the expansion
and form a sum of
terms with the largest
out of this expansion.
The second one (theorem 3.3) states that nonlinear
‐term approximations with regard to two dictionaries: the Haar basis and the set of all characteristic functions of intervals
are equivalent in a very strong sense.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | |
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