Best Basis Selection for Approximation in L _p

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 .

Authors and Affiliations

1. Department of Mathematics University of South Carolina Columbia, SC 29208, USA devore@math.sc.edu, , , , , , US

   Ronald DeVore

2. Department of Mathematics Texas A&M University College Station, TX 77843, USA gpetrova@math.tamu.edu, , , , , , US

   Guergana Petrova

3. Department of Mathematics University of South Carolina Columbia, SC 29208, USA temlyak@math.sc.edu, , , , , , US

   Vladimir Temlyakov

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