Derivation of an upper bound of the constant in the error bound for a near best m-term approximation

2009/10/07 by Wolfgang Karcher, Karcher, Wolfgang, Hans‐Peter Scheffler +3
Computer Science · Engineering · Mathematics · #41A50 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Image and Signal Denoising Methods #Mathematical Approximation and Integration #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.0910.1202

openalex publication_date 2009/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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