We define various algorithms for greedy approximations by elements of an arbitrary set ##IMG## [http://ej.iop.org/images/1064-5632/84/2/246/IZV_84_2_246ieqn1.gif] {$M$} in a Banach space. We study the convergence of these algorithms in a Hilbert space under various geometric conditions on ##IMG## [http://ej.iop.org/images/1064-5632/84/2/246/IZV_84_2_246ieqn1.gif] {$M$} . As a consequence, we obtain sufficient conditions for the additive semigroup generated by ##IMG## [http://ej.iop.org/images/1064-5632/84/2/246/IZV_84_2_246ieqn1.gif] {$M$} to be dense.

中文翻译：

---

任意集的贪婪近似

我们通过任意集合## IMG ## [http://ej.iop.org/images/1064-5632/84/2/246/IZV_84_2_246ieqn1.gif] {$ M $}来定义用于贪婪近似的各种算法在Banach空间中。我们在## IMG ## [http://ej.iop.org/images/1064-5632/84/2/246/IZV_84_2_246ieqn1.gif] {$ M $}。结果，我们为## IMG ## [http://ej.iop.org/images/1064-5632/84/2/246/IZV_84_2_246ieqn1.gif] {$ M $ }要密集。