An optimal order a posteriori parameter choice strategy with modified Newton iterative scheme for solving nonlinear ill-posed operator equations

2017 ◽  
Vol 8 (4) ◽  
pp. 342
Author(s):  
D. Pradeep ◽  
M.P. Rajan
Keyword(s):  
Iterative Scheme ◽  
Optimal Order ◽  
A Posteriori ◽  
Parameter Choice ◽  
Operator Equations ◽  
Choice Strategy ◽  
A Posteriori Parameter Choice ◽  
Ill Posed ◽  
Parameter Choice Strategy

scholarly journals An optimal order yielding discrepancy principle for simplified regularization of ill-posed problems in Hilbert scales

2003 ◽  
Vol 2003 (39) ◽  
pp. 2487-2499 ◽  
Author(s):  
Santhosh George ◽  
M. Thamban Nair
Keyword(s):  
Approximate Solution ◽  
Hilbert Spaces ◽  
Regularization Parameter ◽  
Optimal Order ◽  
Discrepancy Principle ◽  
Parameter Choice ◽  
Bounded Linear ◽  
Choice Strategy ◽  
Ill Posed ◽  
Parameter Choice Strategy

Recently, Tautenhahn and Hämarik (1999) have considered a monotone rule as a parameter choice strategy for choosing the regularization parameter while considering approximate solution of an ill-posed operator equationTx=y, whereTis a bounded linear operator between Hilbert spaces. Motivated by this, we propose a new discrepancy principle for the simplified regularization, in the setting of Hilbert scales, whenTis a positive and selfadjoint operator. When the datayis known only approximately, our method provides optimal order under certain natural assumptions on the ill-posedness of the equation and smoothness of the solution. The result, in fact, improves an earlier work of the authors (1997).

Sign in / Sign up

Export Citation Format

Share Document