LAVRENTIEV'S REGULARIZATION METHOD FOR NONLINEAR ILL-POSED EQUATIONS IN BANACH SPACES

被引：4

作者：

George, Santhosh ^{[1
]}

Sreedeep, C. D. ^{[1
]}

机构：

[1] NIT Karnataka, Dept Math & Computat Sci, Mangaluru 575025, India

来源：

ACTA MATHEMATICA SCIENTIA | 2018年 / 38卷 / 01期

关键词：

nonlinear ill-posed problem; Banach space; Lavrentiev regularization; m-accretive mappings; adaptive parameter choice strategy;

D O I：

10.1016/S0252-9602(17)30133-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we deal with nonlinear ill-posed problems involving m-accretive mappings in Banach spaces. We consider a derivative and inverse free method for the implementation of Lavrentiev regularization method. Using general Holder type source condition we obtain an optimal order error estimate. Also we consider the adaptive parameter choice strategy proposed by Pereverzev and Schock (2005) for choosing the regularization parameter.

引用

页码：303 / 314

页数：12

共 50 条

[1] LAVRENTIEV'S REGULARIZATION METHOD FOR NONLINEAR ILL-POSED EQUATIONS IN BANACH SPACES
Santhosh GEORGE
C.D.SREEDEEP
[J]. Acta Mathematica Scientia, 2018, (01) : 303 - 314
[2] On the method of Lavrentiev regularization for nonlinear ill-posed problems
Tautenhahn, U
[J]. INVERSE PROBLEMS, 2002, 18 (01) : 191 - 207
[3] A New Parameter Choice Strategy for Lavrentiev Regularization Method for Nonlinear Ill-Posed Equations
George, Santhosh
Padikkal, Jidesh
Remesh, Krishnendu
Argyros, Ioannis K.
[J]. MATHEMATICS, 2022, 10 (18)
[4] ITERATIVE LAVRENTIEV REGULARIZATION METHOD UNDER A HEURISTIC RULE FOR NONLINEAR ILL-POSED OPERATOR EQUATIONS
Mahale, Pallavi
Singh, Ankit
[J]. ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS, 2023, 58 : 450 - 469
[5] Simplified Iterated Lavrentiev Regularization for Nonlinear Ill-Posed Monotone Operator Equations
Mahale, Pallavi
[J]. COMPUTATIONAL METHODS IN APPLIED MATHEMATICS, 2017, 17 (02) : 269 - 285
[6] Regularization and convergence for ill-posed backward evolution equations in Banach spaces
Chen, De-Han
Hofmann, Bernd
Zou, Jun
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 265 (08) : 3533 - 3566
[7] A derivative free iterative method for the implementation of Lavrentiev regularization method for ill-posed equations
Vorkady S. Shubha
Santhosh George
P. Jidesh
[J]. Numerical Algorithms, 2015, 68 : 289 - 304
[8] REGULARIZATION FOR THE PROBLEM OF FINDING A SOLUTION OF A SYSTEM OF NONLINEAR MONOTONE ILL-POSED EQUATIONS IN BANACH SPACES
Tran Thi Huong
Kim, Jong Kyu
Nguyen Thi Thu Thuy
[J]. JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2018, 55 (04) : 849 - 875
[9] A derivative free iterative method for the implementation of Lavrentiev regularization method for ill-posed equations
Shubha, Vorkady S.
George, Santhosh
Jidesh, P.
[J]. NUMERICAL ALGORITHMS, 2015, 68 (02) : 289 - 304
[10] An analysis of Lavrentiev regularization method and Newton type process for nonlinear ill-posed problems
Vasin, Vladmir
George, Santhosh
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2014, 230 : 406 - 413

← 1 2 3 4 5 →