scholarly journals A modified Newton–Lavrentiev regularization for nonlinear ill-posed Hammerstein-type operator equations

2008 ◽  
Vol 24 (2) ◽  
pp. 228-240 ◽  
Author(s):  
Santhosh George ◽  
M. Thamban Nair
Keyword(s):  
Type Operator ◽  
Operator Equations ◽  
Lavrentiev Regularization ◽  
Ill Posed

Newton Lavrentiev regularization for ill-posed operator equations in Hilbert scales

2013 ◽  
Vol 219 (24) ◽  
pp. 11191-11197 ◽  
Author(s):  
Santhosh George ◽  
Suresan Pareth ◽  
M. Kunhanandan
Keyword(s):  
Operator Equations ◽  
Lavrentiev Regularization ◽  
Ill Posed

scholarly journals A two step newton type iteration for ill-posed Hammerstein type operator equations in Hilbert scales

2014 ◽  
Vol 26 (1) ◽  
pp. 91-116
Author(s):  
Monnanda Erappa Shobha ◽  
Santhosh George ◽  
M. Kunhanandan
Keyword(s):  
Type Operator ◽  
Operator Equations ◽  
Ill Posed

M. A. Krasnosel'skii Theorem and Iterative Methods for Solving Ill-Posed Linear Problems with a Self-Adjoint Operator

2015 ◽  
Vol 15 (3) ◽  
pp. 373-389
Author(s):  
Oleg Matysik ◽  
Petr Zabreiko
Keyword(s):  
Hilbert Space ◽  
Iterative Methods ◽  
Critical Case ◽  
Adjoint Operator ◽  
Successive Approximations ◽  
Operator Equations ◽  
Ill Posed ◽  
Linear Problems ◽  
Adjoint Operators ◽  
Linear Operator Equations

AbstractThe paper deals with iterative methods for solving linear operator equations ${x = Bx + f}$ and ${Ax = f}$ with self-adjoint operators in Hilbert space X in the critical case when ${\rho (B) = 1}$ and ${0 \in \operatorname{Sp} A}$. The results obtained are based on a theorem by M. A. Krasnosel'skii on the convergence of the successive approximations, their modifications and refinements.

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