The Regularized Global GMERR Method for Solving Large-Scale Linear Discrete Ill-Posed Problems

被引：0
作者：
Zhang, Hui [1 ]
Dai, Hua [1 ]
机构：
[1] Nanjing Univ Aeronaut & Astronaut, Sch Math, Nanjing 210016, Peoples R China
来源：
EAST ASIAN JOURNAL ON APPLIED MATHEMATICS | 2024年 / 14卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Linear discrete ill-posed problems; multiple right-hand sides; global GMERR method; regularizing properties; TIKHONOV REGULARIZATION; LEAST-SQUARES; ITERATIVE REGULARIZATION; ALGORITHM; GMRES; SYSTEMS; SUBSPACE; LSQR; LSMR;
D O I：
10.4208/eajam.2023-161.081023
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For the large-scale linear discrete ill -posed problems with multiple right-hand sides, the global Krylov subspace iterative methods have received a lot of attention. In this paper, we analyze the regularizing properties of the global generalized minimum error method (GMERR), and develop a regularized global GMERR method for solving linear discrete ill -posed problems with multiple right-hand sides. The efficiency of the proposed method is confirmed by the numerical experiments on test matrices.
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收藏
页码：874 / 894
页数：21
相关论文
共 53 条
[1]  
[Anonymous], 2012, Methods for Solving Incorrectly Posed Problems
[2]  
Bai Z.-Z., 2021, Matrix Analysis and Computations
[3]   Motivations and realizations of Krylov subspace methods for large sparse linear systems [J].
Bai, Zhong-Zhi .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 283 :71-78
[4]   The block Lanczos algorithm for linear ill-posed problems [J].
Bentbib, A. H. ;
El Guide, M. ;
Jbilou, K. .
CALCOLO, 2017, 54 (03) :711-732
[5]   Global Golub-Kahan bidiagonalization applied to large discrete ill-posed problems [J].
Bentbib, A. H. ;
El Guide, M. ;
Jbilou, K. ;
Reichel, L. .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2017, 322 :46-56
[6]   A global Lanczos method for image restoration [J].
Bentbib, A. H. ;
El Guide, M. ;
Jbilou, K. ;
Reichel, L. .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2016, 300 :233-244
[7]  
BJORCK A, 1988, BIT, V28, P659, DOI 10.1007/BF01941141
[8]  
Bjorck A., 1996, NUMERICAL METHODS LE
[9]   A generalized global Arnoldi method for ill-posed matrix equations [J].
Bouhamidi, A. ;
Jbilou, K. ;
Reichel, L. ;
Sadok, H. .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2012, 236 (08) :2078-2089
[10]   On the regularizing properties of the GMRES method [J].
Calvetti, D ;
Lewis, B ;
Reichel, L .
NUMERISCHE MATHEMATIK, 2002, 91 (04) :605-625
123456