Condition numbers and perturbation analysis for the Tikhonov regularization of discrete ill-posed problems

被引：15
|
作者：
Chu, Delin [4 ]
Lin, Lijing [3 ]
Tan, Roger C. E. [4 ]
Wei, Yimin [1 ,2 ]
机构：
[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
[2] Fudan Univ, Shanghai Key Lab Contemporary Appl Math, Shanghai 200433, Peoples R China
[3] Fudan Univ, Inst Math Sci, Shanghai 200433, Peoples R China
[4] Natl Univ Singapore, Dept Math, Singapore 117543, Singapore
来源：
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS | 2011年 / 18卷 / 01期
基金：
中国国家自然科学基金;
关键词：
linear least squares; condition number; Tikhonov regularization; perturbation; LINEAR LEAST-SQUARES; SINGULAR VALUE DECOMPOSITION; NUMERICAL SOLUTION; COMPONENTWISE; BOUNDS;
D O I：
10.1002/nla.702
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
One of the most successful methods for solving the least-squares problem min(x) parallel to A(x) - b parallel to(2) with a highly ill-conditioned or rank deficient coefficient matrix A is the method of Tikhonov regularization. In this paper, we derive the normwise, mixed and componentwise condition numbers and componentwise perturbation bounds for the Tikhonov regularization. Our results are sharper than the known results. Some numerical examples are given to illustrate our results. Copyright (C) 2010 John Wiley & Sons, Ltd.
引用
收藏
页码：87 / 103
页数：17
相关论文
共 50 条
  • [21] Design of Graph Filter in Ill-Posed Condition Using Tikhonov Regularization
    Tseng, Chien-Cheng
    Lee, Su-Ling
    2015 IEEE INTERNATIONAL CONFERENCE ON CONSUMER ELECTRONICS - TAIWAN (ICCE-TW), 2015, : 406 - 407
  • [22] 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
  • [23] THE DISCRETE PICARD CONDITION FOR DISCRETE ILL-POSED PROBLEMS
    HANSEN, PC
    BIT NUMERICAL MATHEMATICS, 1990, 30 (04) : 658 - 672
  • [24] 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
  • [25] Regularization parameter determination for discrete ill-posed problems
    Hochstenbach, M. E.
    Reichel, L.
    Rodriguez, G.
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 273 : 132 - 149
  • [26] 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)
  • [27] LOGARITHMIC CONVERGENCE RATES OF TIKHONOV REGULARIZATION FOR NONLINEAR ILL-POSED PROBLEMS
    Yang, Xiao-Mei
    Deng, Zhi-Liang
    2012 INTERNATIONAL CONFERENCE ON WAVELET ACTIVE MEDIA TECHNOLOGY AND INFORMATION PROCESSING (LCWAMTIP), 2012, : 359 - 362
  • [28] MODIFIED TIKHONOV REGULARIZATION FOR NONLINEAR ILL-POSED PROBLEMS IN BANACH SPECES
    Neubauer, Andreas
    JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS, 2010, 22 (02) : 341 - 351
  • [29] The Lagrange method for the regularization of discrete ill-posed problems
    G. Landi
    Computational Optimization and Applications, 2008, 39 : 347 - 368
  • [30] A wavelet multilevel method for ill-posed problems stabilized by Tikhonov regularization
    Rieder, A
    NUMERISCHE MATHEMATIK, 1997, 75 (04) : 501 - 522
12345