Derivation of an upper bound of the constant in the error bound for a near best m-term approximation
Provides a concrete constant for a known error bound in approximation theory, which is an incremental improvement.
The paper derives an explicit upper bound for the constant in the error bound for near best m-term approximation using the Haar system, which was previously not given explicitly.
In the paper "The best m-term approximation and greedy algorithms" (V. N. Temlyakov), an error bound for a near best m-term approximation of a function g in L^p([0,1]^d) is provided, using a basis L^p-equivalent to the Haar system, where p is greater than one and less than infinity and d is a natural number. The bound includes a constant C(p) that is not given explicitly. The goal of this paper is to find an upper bound of the constant for the Haar system.