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Weak greedy algorithms. (English) Zbl 0964.65009

Theoretical aspects of the efficiency of \(M\)-term approximation is studied for “weak” greedy algorithms. These are defined by weaker assumptions than their known analogs: the pure greedy algorithm, an orthogonal greedy algorithm, and a relaxed greedy algorithm. Convergence theorems and rates of approximation by these algorithms are proved. The results apply to approximation from an arbitrary dictionary in a Hilbert space.

MSC:

65D15 Algorithms for approximation of functions
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
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