Iteratively regularized methods for irregular nonlinear operator equations with a normally solvable derivative at the solution

DOI10.1134/S0965542516090098zbMath1444.47066MaRDI QIDQ519681

Mikhail Yu. Kokurin

Publication date: 5 April 2017

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

inverse problemHilbert spacecompact operatorTikhonov regularizationdiscrepancy principleregularization methodill-posed problemsource conditionnormally solvable operatorGauß-Newton-type methodmethod of asymptotic regularization

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Nonlinear ill-posed problems (47J06) Numerical solutions to equations with nonlinear operators (65J15) Numerical methods for ill-posed problems for integral equations (65R30) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical methods for inverse problems for integral equations (65R32) Numerical solution to inverse problems in abstract spaces (65J22)

Related Items (4)

Iteratively regularized Gauss-Newton type methods for approximating quasi-solutions of irregular nonlinear operator equations in Hilbert space with an application to COVID-19 epidemic dynamics ⋮ A study of frozen iteratively regularized Gauss-Newton algorithm for nonlinear ill-posed problems under generalized normal solvability condition ⋮ On regularization procedures with linear accuracy estimates of approximations ⋮ A study of a posteriori stopping in iteratively regularized Gauss-Newton-type methods for approximating quasi-solutions of irregular operator equations

Cites Work

• The global search in the Tikhonov scheme
• Iterative methods of stochastic approximation for solving non-regular nonlinear operator equations
• Iterative regularization methods for nonlinear ill-posed problems
• Can an a priori error estimate for an approximate solution of an ill-posed problem be comparable with the error in data?
• Convexity of the Tikhonov functional and iteratively regularized methods for solving irregular nonlinear operator equations
• Definitions and examples of inverse and ill-posed problems
• ON APPLICATION OF GENERALIZED DISCREPANCY PRINCIPLE TO ITERATIVE METHODS FOR NONLINEAR ILL-POSED PROBLEMS
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