BALANCING PRINCIPLE FOR ITERATED TIKHONOV METHOD OF SEVERELY ILL-POSED PROBLEMS

被引：0

作者：

Myleiko, Ganna ^{[1
]}

Solodky, Sergei ^{[1
]}

机构：

[1] Natl Acad Sci, Inst Math, 3 Tereschenkivska Str, UA-01601 Kiev, Ukraine

来源：

JOURNAL OF NUMERICAL AND APPLIED MATHEMATICS | 2012年 / 3卷 / 109期

关键词：

Severely ill-posed problem; balancing principle; iterated Tikhonov method;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Considered in this paper are the problem of approximate solving severely ill-posed problems with perturbed input data. In oder to regularize these problems the iterated Tikhonov method with balancing principle as stop rule was applied. For this suggesting approach an order of accuracy on the class of problems under investigation was found.

引用

页码：72 / 88

页数：17

共 50 条

[1] About Regularization of Severely Ill-Posed Problems by Standard Tikhonov's Method with the Balancing Principle
Solodky, Sergei G.
Myleiko, Ganna L.
[J]. MATHEMATICAL MODELLING AND ANALYSIS, 2014, 19 (02) : 199 - 215
[2] On inertial iterated Tikhonov methods for solving ill-posed problems
Rabelo, J. C.
Leitao, A.
Madureira, A. L.
[J]. INVERSE PROBLEMS, 2024, 40 (03)
[3] Spectral method for ill-posed problems based on the balancing principle
Xiong, Xiangtuan
Fan, Xiaoyan
Li, Ming
[J]. INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, 2015, 23 (02) : 292 - 306
[4] A relaxed iterated Tikhonov regularization for linear ill-posed inverse problems
Chang, Weike
D'Ascenzo, Nicola
Xie, Qingguo
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 530 (02)
[5] ON THE CHOICE OF THE REGULARIZATION PARAMETER FOR ITERATED TIKHONOV REGULARIZATION OF ILL-POSED PROBLEMS
ENGL, HW
[J]. JOURNAL OF APPROXIMATION THEORY, 1987, 49 (01) : 55 - 63
[6] Nonstationary iterated Tikhonov regularization for ill-posed problems in Banach spaces
Jin, Qinian
Stals, Linda
[J]. INVERSE PROBLEMS, 2012, 28 (10)
[7] The principle of penalized empirical risk in severely ill-posed problems
Yu Golubev
[J]. Probability Theory and Related Fields, 2004, 130 : 18 - 38
[8] The principle of penalized empirical risk in severely ill-posed problems
Golubev, Y
[J]. PROBABILITY THEORY AND RELATED FIELDS, 2004, 130 (01) : 18 - 38
[9] Tikhonov regularization for nonlinear ill-posed problems
Hou, ZY
Jin, QN
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 28 (11) : 1799 - 1809
[10] A predictor-corrector iterated Tikhonov regularization for linear ill-posed inverse problems
Liu, Wen
Wu, Chuansheng
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2013, 221 : 802 - 818

← 1 2 3 4 5 →