Convex Tikhonov regularization in Banach spaces: New results on convergence rates

被引:9
|
作者
Kindermann, Stefan [1 ]
机构
[1] Johannes Kepler Univ Linz, Altenbergerstr 69, A-4040 Linz, Austria
来源
关键词
Tikhonov regularization; convergence rates; Bregman distance; variational regularization;
D O I
10.1515/jiip-2015-0038
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Tikhonov regularization in Banach spaces with convex penalty and convex fidelity term for linear ill-posed operator equations is studied. As a main result, convergence rates in terms of the Bregman distance of the regularized solution to the exact solution is proven by imposing a generalization of the established variational inequality conditions on the exact solution. This condition only involves a decay rate of the difference of the penalty functionals in terms of the residual.
引用
收藏
页码:341 / 350
页数:10
相关论文
共 50 条
  • [21] Mixed Tikhonov regularization in Banach spaces based on domain decomposition
    Cimrak, Ivan
    Melicher, Valdemar
    APPLIED MATHEMATICS AND COMPUTATION, 2012, 218 (23) : 11583 - 11596
  • [22] Convergence rates for Tikhonov regularization based on range inclusions
    Hofmann, B
    Yamamoto, M
    INVERSE PROBLEMS, 2005, 21 (03) : 805 - 820
  • [23] Tikhonov regularization for a class of generalized hemivariational inequality in Banach spaces
    Liu, Min
    Min, Chao
    Tang, Guo-ji
    Xiao, Yi-bin
    OPTIMIZATION, 2023, 72 (06) : 1643 - 1663
  • [24] Tikhonov regularization method for a system of equilibrium problems in Banach spaces
    Buong N.
    Hai Ha D.T.
    Ukrainian Mathematical Journal, 2009, 61 (8) : 1302 - 1310
  • [25] Convergence rates of convex variational regularization
    Burger, M
    Osher, S
    INVERSE PROBLEMS, 2004, 20 (05) : 1411 - 1421
  • [26] Optimal convergence rates for Tikhonov regularization in Besov scales
    Lorenz, D. A.
    Trede, D.
    JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2009, 17 (01): : 69 - 76
  • [27] CONVERGENCE OF HEURISTIC PARAMETER CHOICE RULES FOR CONVEX TIKHONOV REGULARIZATION
    Kindermann, Stefan
    Raik, Kemal
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2020, 58 (03) : 1773 - 1800
  • [28] A note on logarithmic convergence rates for nonlinear Tikhonov regularization
    Kaltenbacher, B.
    JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2008, 16 (01): : 79 - 88
  • [29] Optimal convergence rates for Tikhonov regularization in Besov scales
    Lorenz, D. A.
    Trede, D.
    INVERSE PROBLEMS, 2008, 24 (05)
  • [30] CONVERGENCE RATES FOR OVERSMOOTHING BANACH SPACE REGULARIZATION
    Miller, Philip
    Hohage, Thorsten
    ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS, 2022, 57 : 101 - 126