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<p>We present a brief survey on two intertwined themes: convergence of consecutive projections onto a family of closed convex sets with nonempty intersection and greedy algorithms with respect to a dictionary in a Hilbert space. Consecutive projections onto a family of hyperplanes can be interpreted as the work of a weak greedy algorithm with respect to the dictionary consisting of vectors normal to those hyperplanes. This observation suggests the use of methods developed in the theory of greedy approximations to study the convergence of consecutive projections, and vice versa. Bibliography: 64 titles.</p>

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CONSECUTIVE PROJECTIONS AND GREEDY APPROXIMATION IN HILBERT SPACE

  • 期刊论文

  • 发表日期：

    2026年4月23日

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  • Petr Borodin,
  • Eva Kopecká

摘要

We present a brief survey on two intertwined themes: convergence of consecutive projections onto a family of closed convex sets with nonempty intersection and greedy algorithms with respect to a dictionary in a Hilbert space. Consecutive projections onto a family of hyperplanes can be interpreted as the work of a weak greedy algorithm with respect to the dictionary consisting of vectors normal to those hyperplanes. This observation suggests the use of methods developed in the theory of greedy approximations to study the convergence of consecutive projections, and vice versa. Bibliography: 64 titles.