Vector greedy algorithms

Adam Lutoborski, Vladimir N. Temlyakov

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

Our objective is to study nonlinear approximation with regard to redundant systems. Redundancy on the one hand offers much promise for greater efficiency in terms of approximation rate, but on the other hand gives rise to highly nontrivial theoretical and practical problems. Greedy-type approximations proved to be convenient and efficient ways of constructing m-term approximants. We introduce and study vector greedy algorithms that are designed with aim of constructing mth greedy approximants simultaneously for a given finite number of elements. We prove convergence theorems and obtain some estimates for the rate of convergence of vector greedy algorithms when elements come from certain classes.

Original languageEnglish (US)
Pages (from-to)458-473
Number of pages16
JournalJournal of Complexity
Volume19
Issue number4
DOIs
StatePublished - Aug 2003

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Statistics and Probability
  • Numerical Analysis
  • Mathematics(all)
  • Control and Optimization
  • Applied Mathematics

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