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Greedy approximation and the multivariate Haar system

A. Kamont, V. N. Temlyakov (2004)

Studia Mathematica

We study nonlinear m-term approximation in a Banach space with regard to a basis. It is known that in the case of a greedy basis (like the Haar basis in L p ( [ 0 , 1 ] ) , 1 < p < ∞) a greedy type algorithm realizes nearly best m-term approximation for any individual function. In this paper we generalize this result in two directions. First, instead of a greedy algorithm we consider a weak greedy algorithm. Second, we study in detail unconditional nongreedy bases (like the multivariate Haar basis d = × . . . × in L p ( [ 0 , 1 ] d ) ,...

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