Best Basis Selection for Approximation in Lp

Abstract. We study the approximation of a function class F in Lp 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 Lp . 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 L2 to Lp , p\neq 2 .

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