Large-scale Tikhonov regularization via reduction by orthogonal projection

被引：42
|
作者：
Lampe, Joerg [1 ]
Reichel, Lothar [2 ]
Voss, Heinrich [1 ]
机构：
[1] Hamburg Univ Technol, Inst Numer Simulat, D-21071 Hamburg, Germany
[2] Kent State Univ, Dept Math Sci, Kent, OH 44242 USA
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2012年 / 436卷 / 08期
关键词：
Least squares; General-form Tikhonov regularization; Discrepancy principle; Ill-posedness; L-CURVE; ALGORITHM;
D O I：
10.1016/j.laa.2011.07.019
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper presents a new approach to computing an approximate solution of Tikhonov-regularized large-scale ill-posed least-squares problems with a general regularization matrix. The iterative method applies a sequence of projections onto generalized Krylov subspaces. A suitable value of the regularization parameter is determined by the discrepancy principle. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码：2845 / 2865
页数：21
相关论文
共 50 条
  • [1] Large-scale Tikhonov regularization of total least squares
    Lampe, Joerg
    Voss, Heinrich
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2012, 238 : 95 - 108
  • [2] A HYBRID LSMR ALGORITHM FOR LARGE-SCALE TIKHONOV REGULARIZATION
    Chung, Julianne
    Palmer, Katrina
    SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2015, 37 (05): : S562 - S580
  • [3] Regularization parameter estimation for large-scale Tikhonov regularization using a priori information
    Renaut, Rosemary A.
    Hnetynkova, Iveta
    Mead, Jodi
    COMPUTATIONAL STATISTICS & DATA ANALYSIS, 2010, 54 (12) : 3430 - 3445
  • [4] Generalized Tikhonov regularization method for large-scale linear inverse problems
    Zhang, Di
    Huang, Ting-Zhu
    JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2013, 15 (07) : 1317 - 1331
  • [5] On the choice of subspace for large-scale Tikhonov regularization problems in general form
    Huang, Guangxin
    Reichel, Lothar
    Yin, Feng
    NUMERICAL ALGORITHMS, 2019, 81 (01) : 33 - 55
  • [6] On the choice of subspace for large-scale Tikhonov regularization problems in general form
    Guangxin Huang
    Lothar Reichel
    Feng Yin
    Numerical Algorithms, 2019, 81 : 33 - 55
  • [7] Projected Tikhonov Regularization of Large-Scale Discrete Ill-Posed Problems
    David R. Martin
    Lothar Reichel
    Journal of Scientific Computing, 2013, 56 : 471 - 493
  • [8] Projected Tikhonov Regularization of Large-Scale Discrete Ill-Posed Problems
    Martin, David R.
    Reichel, Lothar
    JOURNAL OF SCIENTIFIC COMPUTING, 2013, 56 (03) : 471 - 493
  • [9] Tikhonov regularization via flexible Arnoldi reduction
    Lothar Reichel
    Xuebo Yu
    BIT Numerical Mathematics, 2015, 55 : 1145 - 1168
  • [10] Tikhonov regularization via flexible Arnoldi reduction
    Reichel, Lothar
    Yu, Xuebo
    BIT NUMERICAL MATHEMATICS, 2015, 55 (04) : 1145 - 1168
12345