Convergence of regularized greedy approximations
- Autores: Svetlov I.P.1
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Afiliações:
- Lomonosov Moscow State University
- Edição: Volume 89, Nº 2 (2025)
- Páginas: 114-127
- Seção: Articles
- URL: https://journal-vniispk.ru/1607-0046/article/view/303949
- DOI: https://doi.org/10.4213/im9608
- ID: 303949
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Resumo
We consider a new version of a greedy algorithm in biorthogonal systems in separable Banach spaces.We consider approximations of an element $f$ via $m$-term greedy sum, which isconstructed from the expansion by choosing the first$m$ greatest in absolute value coefficients.It is known that the greedy algorithm does not always converge to the original element.We prove a theorem showing that the new version of a greedy algorithm(called the regularized greedy algorithm) always converges to the original element in Efimov–Stechkin spaces. We also construct examples that show the significance of the conditions of the main theorem.
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Sobre autores
Iurii Svetlov
Lomonosov Moscow State University
Autor responsável pela correspondência
Email: yuri.svetlov@math.msu.ru
without scientific degree, no status
Bibliografia
- V. Temlyakov, Greedy approximation, Cambridge Monogr. Appl. Comput. Math., 20, Cambridge Univ. Press, Cambridge, 2011, xiv+418 pp.
- S. V. Konyagin, V. N. Temlyakov, “A remark on greedy approximation in Banach spaces”, East J. Approx., 5:3 (1999), 365–379
- P. Wojtaszczyk, “Greedy algorithms for general Biorthogonal systems”, J. Approx. Theory, 107:2 (2000), 293–314
- V. N. Temlyakov, “Greedy algorithm and $m$-term trigonometric approximation”, Constr. Approx., 14:4 (1998), 569–587
- Н. В. Ефимов, С. Б. Стечкин, “Аппроксимативная компактность и чебышевские множества”, Докл. АН СССР, 140:3 (1961), 522–524
- I. Singer, “Some remarks on approximative compactness”, Rev. Roumaine Math. Pures Appl., 9 (1964), 167–177
- A. R. Alimov, I. G. Tsar'kov, Geometric approximation theory, Springer Monogr. Math., Springer, Cham, 2021, xxi+508 pp.
- S. J. Dilworth, D. Kutzarova, V. N. Temlyakov, “Convergence of some greedy algorithms in Banach spaces”, J. Fourier Anal. Appl., 8:5 (2002), 489–506
- С. В. Конягин, И. Г. Царьков, “Пространства Ефимова–Стечкина”, Вестн. Моск. ун-та. Сер. 1. Матем., мех., 1986, № 5, 20–27
- А. Н. Колмогоров, С. В. Фомин, Элементы теории функций и функционального анализа, 6-е перераб. изд., Наука, М., 1989, 624 с.
- А. Р. Алимов, И. Г. Царьков, Основы геометрической теории приближений, Часть I. Приближение выпуклыми множествами, Изд. П. Ю. Мархотин, М., 2016, 120 с.
- Б. С. Кашин, А. А. Саакян, Ортогональные ряды, 2-е доп. изд., АФЦ, М., 1999, x+550 с.
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