On the Convergence of a Weak Greedy Algorithm for the Multivariate Haar Basis

被引：3
|
作者：
Dilworth, S. J. [1 ]
Gogyan, S. [2 ]
Kutzarova, Denka [3 ]
机构：
[1] Univ S Carolina, Dept Math, Columbia, SC 29208 USA
[2] Armenian Acad Sci, Inst Math, Yerevan 0019, Armenia
[3] Bulgarian Acad Sci, Inst Math, Sofia, Bulgaria
来源：
CONSTRUCTIVE APPROXIMATION | 2014年 / 39卷 / 02期
基金：
美国国家科学基金会;
关键词：
Greedy algorithms; Weak thresholding; Thresholding greedy algorithm; Branch-greedy; Nonlinear approximation; Multivariate Haar system; Multivariate Haar wavelet; BANACH-SPACES; APPROXIMATION; SYSTEMS;
D O I：
10.1007/s00365-013-9212-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We define a family of weak thresholding greedy algorithms for the multivariate Haar basis for L (1)[0,1] (d) (da parts per thousand yen1). We prove convergence and uniform boundedness of the weak greedy approximants for all faL (1)[0,1] (d) .
引用
收藏
页码：343 / 366
页数：24
相关论文
共 50 条
  • [21] Lebesgue constants for the weak greedy algorithm
    S. J. Dilworth
    D. Kutzarova
    T. Oikhberg
    Revista Matemática Complutense, 2015, 28 : 393 - 409
  • [22] On the convergence of order-preserving weak greedy algorithms
    A. V. Sil’nichenko
    Mathematical Notes, 2008, 84 : 741 - 747
  • [23] On the Convergence of Order-Preserving Weak Greedy Algorithms
    Sil'nichenko, A. V.
    MATHEMATICAL NOTES, 2008, 84 (5-6) : 741 - 747
  • [24] A greedy algorithm for the optimal basis problem
    Oleg Burdakov
    BIT Numerical Mathematics, 1997, 37 : 591 - 599
  • [25] Weak convergence of multivariate fractional processes
    Marinucci, D
    Robinson, PM
    STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2000, 86 (01) : 103 - 120
  • [26] A greedy algorithm for the optimal basis problem
    Burdakov, O
    BIT NUMERICAL MATHEMATICS, 1997, 37 (03) : 591 - 599
  • [27] CONVERGENCE RATES FOR GREEDY ALGORITHMS IN REDUCED BASIS METHODS
    Binev, Peter
    Cohen, Albert
    Dahmen, Wolfgang
    Devore, Ronald
    Petrova, Guergana
    Wojtaszczyk, Przemyslaw
    SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2011, 43 (03) : 1457 - 1472
  • [28] Convergence of Greedy Algorithm in Walsh System in Lp
    Amirkhanyan, G.
    JOURNAL OF CONTEMPORARY MATHEMATICAL ANALYSIS-ARMENIAN ACADEMY OF SCIENCES, 2008, 43 (03): : 127 - 134
  • [29] On the convergence of the order-preserving weak greedy algorithm for subspaces generated by the Szego kernel in the Hardy space
    Speransky, K. S.
    IZVESTIYA OF SARATOV UNIVERSITY MATHEMATICS MECHANICS INFORMATICS, 2021, 21 (03): : 336 - 342
  • [30] Approximation by Egyptian fractions and the weak greedy algorithm
    Chu, Hung Viet
    INDAGATIONES MATHEMATICAE-NEW SERIES, 2023, 34 (06): : 1303 - 1317
12345