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

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (1): 303-314.

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

Santhosh GEORGE, C. D. SREEDEEP

Department of Mathematical and Computational Sciences, NIT Karnataka, Mangaluru-575 025, India

收稿日期:2016-09-06 修回日期:2017-10-18 出版日期:2018-02-25 发布日期:2018-02-25
作者简介:Santhosh GEORGE,E-mail:sgeorge@nitk.edu.in;C.D.SREEDEEP,E-mail:cd.sreedeep@gmail.com

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

Santhosh GEORGE, C. D. SREEDEEP

Department of Mathematical and Computational Sciences, NIT Karnataka, Mangaluru-575 025, India

Received:2016-09-06 Revised:2017-10-18 Online:2018-02-25 Published:2018-02-25

摘要/Abstract

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 Hölder 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.

关键词: nonlinear ill-posed problem, Banach space, Lavrentiev regularization, m-accretive mappings, adaptive parameter choice strategy

Abstract: 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 Hölder 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.

Key words: nonlinear ill-posed problem, Banach space, Lavrentiev regularization, m-accretive mappings, adaptive parameter choice strategy

Santhosh GEORGE, C. D. SREEDEEP. LAVRENTIEV'S REGULARIZATION METHOD FOR NONLINEAR ILL-POSED EQUATIONS IN BANACH SPACES[J]. 数学物理学报(英文版), 2018, 38(1): 303-314.

Santhosh GEORGE, C. D. SREEDEEP. LAVRENTIEV'S REGULARIZATION METHOD FOR NONLINEAR ILL-POSED EQUATIONS IN BANACH SPACES[J]. Acta mathematica scientia,Series B, 2018, 38(1): 303-314.

参考文献

[1] Alber Y I. On solution by the method of regularization for operator equation of the first kind involving accretive mappings in Banach spaces. Differ Equ SSSR, 1975, XI:2242-2248
[2] Alber Y I, Ryazantseva I P. Nonlinear Ill-Posed Problems of Monotone Type. Dordrecht:Springer, 2006
[3] Argyros I K, George S. Iterative regularization methods for nonlinear ill-posed operator equations with m-accretive mappings in Banach spaces. Acta Math Sci, 2015, 35B(6):1318-1324
[4] Buong N. Projection-regularization method and ill-posedness for equations involving accretive operators. Vietnamese Math J, 1992, 20:33-39
[5] Buong N. Convergence rates in regularization under arbitrarily perturbative operators. Annali di Mathematica, 2003, 43(3):323-327
[6] Buong N. Convergence rates in regularization for nonlinear ill-posed equations under m-accretive perturbations. Zh Vychisl Matematiki i Matem Fiziki, 2004, 44:397-402
[7] Buong N. Generalized discrepancy principle and ill-posed equations involving accretive operators. Nonlinear Funct Anal Appl, 2004, 9:73-78
[8] Buong N. On nonlinear ill-posed accretive equations. Southest Asian Bull Math, 2004, 28:1-6
[9] Buong N. Convergence rates in regularization for nonlinear ill-posed equations involving m-accretive mappings in Banach spaces. Appl Math Sci, 2012, 63(6):3109-3117
[10] Buong N, Hung V Q. Newton-Kantorovich iterative regularization for nonlinear ill-posed equations involving accretive operators. Ukrainian Math Zh, 2005, 57:23-30
[11] Hofmann B, Kaltenbacher B, Resmerita E. Lavrentiev's regularization method in Hilbert spaces. Revisited, arXiv:150601803v2[mathNA], 19, 2016
[12] Krasnoselskii M A, Zabreiko P P, Pustylnik E I, Sobolevskii P E. Integral Operators in Spaces of Summable Functions. Leyden:Noordhoff International Publ, 1976
[13] Liu Z H. Browder-Tikhonov regularization of non-coercive ill-posed hemivariational inequalities. Inverse Probl, 2005, 21:13-20
[14] Pereverzyev S, Schock E. On the adaptive selection of the parameter in regularization of ill-posed problems. SIAM J Numer Anal, 2005, 43(5):2060-2076
[15] Semenova E V. Lavrentiev regularization and balancing principle for solving ill-posed problems with monotone operators. Comput Methods Appl Math, 2010, 10(4):444-454
[16] Tautenhahn U. On the method of Lavrentiev regularization for nonlinear ill-posed problems. Inverse Probl, 2002, 18:191-207
[17] Vasin V, George S. An analysis of lavrentiev regularization method and newton type process for nonlinear ill-posed problem. Appl Math Comput, 2014, 230:406-413
[18] Wang J A, Li J, Liu Z H. Regularization methods for nonlinear ill-posed problems with accretive operators. Acta Math Sci, 2008, 28B(1):141-150

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

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

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 10

[1]	Jasbir Singh MANHAS, Ruhan ZHAO. PRODUCTS OF WEIGHTED COMPOSITION AND DIFFERENTIATION OPERATORS INTO WEIGHTED ZYGMUND AND BLOCH SPACES[J]. 数学物理学报(英文版), 2018, 38(4): 1105-1120.
[2]	程立新, 罗思捷. YET ON LINEAR STRUCTURES OF NORM-ATTAINING FUNCTIONALS ON ASPLUND SPACES[J]. 数学物理学报(英文版), 2018, 38(1): 151-156.
[3]	王紫, 王玉文. A NEW PERTURBATION THEOREM FOR MOORE-PENROSE METRIC GENERALIZED INVERSE OF BOUNDED LINEAR OPERATORS IN BANACH SPACES[J]. 数学物理学报(英文版), 2017, 37(6): 1619-1631.
[4]	邱德华, ?陈平炎, Volodin ANDREI. COMPLETE MOMENT CONVERGENCE FOR L^P-MIXINGALES[J]. 数学物理学报(英文版), 2017, 37(5): 1319-1330.
[5]	秦小龙, Sun Young CHO. CONVERGENCE ANALYSIS OF A MONOTONE PROJECTION ALGORITHM IN REFLEXIVE BANACH SPACES[J]. 数学物理学报(英文版), 2017, 37(2): 488-502.
[6]	Kazuhide NAKAJO. IMPROVED GRAOIENT METHOD FOR MONOTONE AND LIPSCHITZ CONTINUOUS MAPPINGS IN BANACH SPACES[J]. 数学物理学报(英文版), 2017, 37(2): 342-354.
[7]	张石生, 王林, 秦丽娟, 马招丽. STRONGLY CONVERGENT ITERATIVE METHODS FOR SPLIT EQUALITY VARIATIONAL INCLUSION PROBLEMS IN BANACH SPACES[J]. 数学物理学报(英文版), 2016, 36(6): 1641-1650.
[8]	朱胜, 黄建华. STRONG CONVERGENCE THEOREMS FOR EQUILIBRIUM PROBLEM AND BREGMAN TOTALLY QUASI-ASYMPTOTICALLY NONEXPANSIVE MAPPING IN BANACH SPACES[J]. 数学物理学报(英文版), 2016, 36(5): 1433-1444.
[9]	鲍玲鑫. ON WEAK FILTER CONVERGENCE AND THE RADON-RIESZ TYPE THEOREM[J]. 数学物理学报(英文版), 2016, 36(1): 215-219.
[10]	Jasbir Singh MANHAS, Ruhan ZHAO. ESSENTIAL NORMS OF PRODUCTS OF WEIGHTED COMPOSITION OPERATORS AND DIFFERENTIATION OPERATORS BETWEEN BANACH SPACES OF ANALYTIC FUNCTIONS[J]. 数学物理学报(英文版), 2015, 35(6): 1401-1410.
[11]	Choonkil PARK. QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN BANACH SPACES[J]. 数学物理学报(英文版), 2015, 35(6): 1501-1510.
[12]	Eric U. OFOEDU, Charles E. ONYI. APPROXIMATION OF COMMON FIXED POINT OF FAMILIES OF NONLINEAR MAPPINGS WITH APPLICATIONS[J]. 数学物理学报(英文版), 2015, 35(5): 1225-1240.
[13]	Yekini SHEHU. CONVERGENCE ANALYSIS FOR SYSTEM OF EQUILIBRIUM PROBLEMS AND LEFT BREGMAN STRONGLY RELATIVELY NONEXPANSIVE MAPPING[J]. 数学物理学报(英文版), 2014, 34(4): 1081-1097.
[14]	Yekini SHEHU. APPROXIMATION OF FIXED POINTS AND VARIATIONAL SOLUTIONS FOR PSEUDO-CONTRACTIVE MAPPINGS IN#br# BANACH SPACES[J]. 数学物理学报(英文版), 2014, 34(2): 409-423.
[15]	B. Yousefi, Sh. Khoshdel. REFLEXIVITY OF POWERS OF THE MULTIPLICATION OPERATOR ON SPECIAL FUNCTION SPACES[J]. 数学物理学报(英文版), 2012, 32(6): 2279-2284.