Best Basis Selection for Approximation in L p |
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| Authors: | Ronald DeVore Guergana Petrova and Vladimir Temlyakov |
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| Institution: | (1) Department of Mathematics University of South Carolina Columbia, SC 29208, USA devore@math.sc.edu, US;(2) Department of Mathematics Texas A&M University College Station, TX 77843, USA gpetrova@math.tamu.edu, US;(3) Department of Mathematics University of South Carolina Columbia, SC 29208, USA temlyak@math.sc.edu, US |
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| Abstract: | We study the approximation of a function class F in L
p
by choosing first a basis B and then using n -term approximation with the elements of B . Into the competition for best bases we enter all greedy (i.e., democratic and unconditional 20]) bases for L
p
. We show that if the function class F is well-oriented with respect to a particular basis B then, in a certain sense, this basis is the best choice for this type of approximation. Our results extend the recent results
of Donoho 9] from L
2
to L
p
, p\neq 2 . |
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| Keywords: | , Best basis, n -Term approximation, Degree of approximation, Approximation classes, Democratic bases, Unconditional,,,,,bases, Greedy bases, AMS Classification, 42C40, 46B70, 26B35, 42B25, |
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