Simultaneous approximation by greedy algorithms

D. Leviatan, V. N. Temlyakov

Research output: Contribution to journalArticlepeer-review

Abstract

We study nonlinear m-term approximation with regard to a redundant dictionary D in a Hilbert space H. It is known that the Pure Greedy Algorithm (or, more generally, the Weak Greedy Algorithm) provides for each f H and any dictionary D an expansion into a series f = ∑j=1∞cj(f) ψj(f), ψj(f)∈ D, j = 1, 2,..., with the Parseval property: ∥f∥2 = ∑j|c j(f)|2. Following the paper of A. Lutoborski and the second author we study analogs of the above expansions for a given finite number of functions f 1,.∈.∈.,f N with a requirement that the dictionary elements φj of these expansions are the same for all f i, i=1,.∈.∈.,N. We study convergence and rate of convergence of such expansions which we call simultaneous expansions.

Original languageEnglish
Pages (from-to)73-90
Number of pages18
JournalAdvances in Computational Mathematics
Volume25
Issue number1-3
DOIs
StatePublished - Jul 2006

Keywords

  • Convergence
  • Greedy algorithms
  • Simultaneous approximation

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