Best Basis Selection for Approximation in Lp
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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 ) 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  from L 2 to L p , p
eq 2 . Society for the Foundation of Computational Mathematics 2002.
Foundations of Computational Mathematics
author list (cited authors)
Ronald DeVore, .., Guergana Petrova, .., & Vladimir Temlyakov.