An iterative method to compute minimum norm solutions of ill-posed problems in Hilbert spaces

2019 ◽  
Vol 30 (5-6) ◽  
pp. 797-816
Author(s):  
Meisam Jozi ◽  
Saeed Karimi ◽  
Davod Khojasteh Salkuyeh
Keyword(s):  
Iterative Method ◽  
Hilbert Spaces ◽  
Minimum Norm ◽  
Ill Posed

scholarly journals On monotone ill-posed problems in Hilbert spaces

2016 ◽  
Vol 11 (4) ◽  
pp. 1-11
Author(s):  
Nguyễn Bường
Keyword(s):  
Hilbert Space ◽  
Iterative Method ◽  
Singular Integral ◽  
Hilbert Spaces ◽  
Convergence Rates ◽  
Operator Method ◽  
Singular Integral Equations ◽  
Monotone Operators ◽  
Method Of Regularization ◽  
Ill Posed

The main aim of this paper is to study convergence rates for an operator method of  regularization to solve nonlinear ill-posed problems involving monotone operators in infinite-dimentional Hilbert space without needing closeness conditions. Then these results are presented in form of  combination with finite-dimentional approximations of the space. An iterative method for solving regularized equation is given and  an example in the theory of singular integral equations is considered for illustration.

scholarly journals Newton Type Iteration for Tikhonov Regularization of Nonlinear Ill-Posed Problems in Hilbert Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Monnanda Erappa Shobha ◽  
Santhosh George
Keyword(s):  
Integral Equation ◽  
Iterative Method ◽  
Iterative Scheme ◽  
Initial Guess ◽  
Optimal Order ◽  
Source Condition ◽  
Adaptive Scheme ◽  
Actual Solution ◽  
Ill Posed ◽  
General Source

Recently, Vasin and George (2013) considered an iterative scheme for approximately solving an ill-posed operator equationF(x)=y. In order to improve the error estimate available by Vasin and George (2013), in the present paper we extend the iterative method considered by Vasin and George (2013), in the setting of Hilbert scales. The error estimates obtained under a general source condition onx0-x^(x0is the initial guess andx^is the actual solution), using the adaptive scheme proposed by Pereverzev and Schock (2005), are of optimal order. The algorithm is applied to numerical solution of an integral equation in Numerical Example section.

scholarly journals Construction of minimum-norm fixed points of pseudocontractions in Hilbert spaces

2014 ◽  
Vol 2014 (1) ◽  
pp. 206 ◽  
Author(s):  
Yonghong Yao ◽  
Giuseppe Marino ◽  
Hong-Kun Xu ◽  
Yeong-Cheng Liou
Keyword(s):  
Fixed Points ◽  
Hilbert Spaces ◽  
Minimum Norm

scholarly journals Strong Convergence of a New Iterative Algorithm for Split Monotone Variational Inclusion Problems

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 123 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Qing Yuan
Keyword(s):  
Iterative Method ◽  
Hilbert Spaces ◽  
Optimization Problem ◽  
Variational Inclusion ◽  
Hierarchical Optimization ◽  
Inclusion Problem ◽  
Inclusion Problems ◽  
Infinite Dimensional ◽  
Variational Inclusion Problem ◽  
General Iterative Method

The main aim of this work is to introduce an implicit general iterative method for approximating a solution of a split variational inclusion problem with a hierarchical optimization problem constraint for a countable family of mappings, which are nonexpansive, in the setting of infinite dimensional Hilbert spaces. Convergence theorem of the sequences generated in our proposed implicit algorithm is obtained under some weak assumptions.

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