Greedy algorithms and approximation properties for frames in Hilbert spaces. (English) Zbl 1415.42029
In this article, the authors study the Threshold Greedy Algorithm (TGA) and the Orthogonal Greedy Algorithm (OGA). Approximation properties concerning greedy algorithms are discussed. The convergence rate of greedy algorithms is studied obtaining various results about the upper estimate of the rate of convergence of the TGA and the OGA with regard to frames. The authors also proved some results concerning the error estimate of the OGA.
Reviewer: Virender Dalal (Delhi)
MSC:
| 42C15 | General harmonic expansions, frames |
| 42C30 | Completeness of sets of functions in nontrigonometric harmonic analysis |
| 42C05 | Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis |
| 46B15 | Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces |
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