THE USE OF MOROZOV DISCREPANCY PRINCIPLE FOR TIKHONOV REGULARIZATION FOR SOLVING NONLINEAR ILL-POSED PROBLEMS

被引：96
|
作者：
SCHERZER, O
机构：
[1] Institut für Mathematik, Johannes-Kepler-Universität, Linz Auhof
来源：
COMPUTING | 1993年 / 51卷 / 01期
关键词：
TIKHONOV REGULARIZATION; INVERSE PROBLEMS; ILL-POSED PROBLEMS; PARAMETER IDENTIFICATION;
D O I：
10.1007/BF02243828
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
In this paper we investigate Morozov's Discrepancy Principle for choosing the regularization parameter in Tikhonov regularization for solving nonlinear ill-posed problems. Convergence rates and a saturation property of the regularized solutions, where the regularization parameter is chosen by the discrepancy principle, are investigated. Numerical results are presented to verify the theoretical results.
引用
下载
收藏
页码：45 / 60
页数：16
相关论文
共 50 条
  • [41] Tikhonov regularization with MTRSVD method for solving large-scale discrete ill-posed problems
    Huang, Guangxin
    Liu, Yuanyuan
    Yin, Feng
    Journal of Computational and Applied Mathematics, 2022, 405
  • [42] Tikhonov regularization with MTRSVD method for solving large-scale discrete ill-posed problems
    Huang, Guangxin
    Liu, Yuanyuan
    Yin, Feng
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2022, 405
  • [43] THE MODIFIED TIKHONOV REGULARIZATION METHOD WITH THE SMOOTHED TOTAL VARIATION FOR SOLVING THE LINEAR ILL-POSED PROBLEMS
    Vasin, V. V.
    Belyaev, V. V.
    EURASIAN JOURNAL OF MATHEMATICAL AND COMPUTER APPLICATIONS, 2021, 9 (02): : 88 - 100
  • [44] Solving ill-posed control problems by stabilized finite element methods: an alternative to Tikhonov regularization
    Burman, Erik
    Hansbo, Peter
    Larson, Mats G.
    INVERSE PROBLEMS, 2018, 34 (03)
  • [45] On application of generalized discrepancy principle to iterative methods for nonlinear ill-posed problems
    Bakushinsky, A
    Smirnova, A
    NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2005, 26 (01) : 35 - 48
  • [46] On inertial iterated Tikhonov methods for solving ill-posed problems
    Rabelo, J. C.
    Leitao, A.
    Madureira, A. L.
    INVERSE PROBLEMS, 2024, 40 (03)
  • [47] A CLASS OF DISCREPANCY PRINCIPLES FOR THE SIMPLIFIED REGULARIZATION OF ILL-POSED PROBLEMS
    GEORGE, S
    NAIR, MT
    JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES B-APPLIED MATHEMATICS, 1994, 36 : 242 - 248
  • [48] ON THE REGULARIZATION OF PROJECTION METHODS FOR SOLVING ILL-POSED PROBLEMS
    PLATO, R
    VAINIKKO, G
    NUMERISCHE MATHEMATIK, 1990, 57 (01) : 63 - 79
  • [49] A relaxed iterated Tikhonov regularization for linear ill-posed inverse problems
    Chang, Weike
    D'Ascenzo, Nicola
    Xie, Qingguo
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 530 (02)
  • [50] STRUCTURED CONDITION NUMBERS FOR THE TIKHONOV REGULARIZATION OF DISCRETE ILL-POSED PROBLEMS
    Meng, Lingsheng
    Zheng, Bing
    JOURNAL OF COMPUTATIONAL MATHEMATICS, 2017, 35 (02) : 169 - 186
12345