AN ITERATIVE METHOD FOR TIKHONOV REGULARIZATION WITH A GENERAL LINEAR REGULARIZATION OPERATOR

被引：46

作者：

Hochstenbach, Michiel E. ^{[1
]}

Reichel, Lothar ^{[2
]}

机构：

[1] Eindhoven Univ Technol, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands

[2] Kent State Univ, Dept Math Sci, Kent, OH 44242 USA

来源：

JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS | 2010年 / 22卷 / 03期

关键词：

Discrete ill-posed problem; iterative method; Tikhonov regularization; general linear regularization operator; discrepancy principle; PRECONDITIONED LSQR; SINGULAR-VALUES;

D O I：

10.1216/JIE-2010-22-3-465

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Tikhonov regularization is one of the most popular approaches to solve discrete ill-posed problems with error-contaminated data. A regularization operator and a suitable value of a regularization parameter have to be chosen. This paper describes an iterative method, based on Golub-Kahan bidiagonalization, for solving large-scale Tikhonov minimization problems with a linear regularization operator of general form. The regularization parameter is determined by the discrepancy principle. Computed examples illustrate the performance of the method.

引用

页码：465 / 482

页数：18

共 23 条

[1] THE USE OF AUTO-CORRELATION FOR PSEUDO-RANK DETERMINATION IN NOISY ILL-CONDITIONED LINEAR LEAST-SQUARES PROBLEMS [J].

BAART, ML .

IMA JOURNAL OF NUMERICAL ANALYSIS, 1982, 2 (02) :241-247

[2] Decomposition methods for large linear discrete ill-posed problems [J].

Baglama, James ;

Reichel, Lothar .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 198 (02) :332-343

[3]

Bjorck A, 1996, NUMERICAL METHODS L

[4] An improved preconditioned LSQR for discrete ill-posed problems [J].

Bunse-Gerstner, Angelika ;

Guerra-Ones, Valia ;

de La Vega, Humberto Madrid .

MATHEMATICS AND COMPUTERS IN SIMULATION, 2006, 73 (1-4) :65-75

[5] Invertible smoothing preconditioners for linear discrete ill-posed problems [J].

Calvetti, D ;

Reichel, L ;

Shuibi, A .

APPLIED NUMERICAL MATHEMATICS, 2005, 54 (02) :135-149

[6] Tikhonov regularization of large linear problems [J].

Calvetti, D ;

Reichel, L .

BIT NUMERICAL MATHEMATICS, 2003, 43 (02) :263-283

[7]

Calvetti D, 2002, ELECTRON T NUMER ANA, V14, P20

[8] REORTHOGONALIZATION AND STABLE ALGORITHMS FOR UPDATING GRAM-SCHMIDT QR FACTORIZATION [J].

DANIEL, JW ;

GRAGG, WB ;

KAUFMAN, L ;

STEWART, GW .

MATHEMATICS OF COMPUTATION, 1976, 30 (136) :772-795

[9]

ELDEN L, 1982, BIT, V22, P487, DOI 10.1007/BF01934412

[10]

Engl H. W., 1996, REGULARIZATION INVER

← 1 2 3 →