An analysis of Lavrentiev regularization method and Newton type process for nonlinear ill-posed problems

DOI10.1016/j.amc.2013.12.104zbMath1410.65231OpenAlexW1964006385MaRDI QIDQ1644078

Vladmir Vasin, Santhosh George

Publication date: 21 June 2018

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2013.12.104

zbMATH Keywords

Newton methodill-posed probleminverse gravimetry problemcenter-type Lipschitz conditionLavrentiev regularization method

Mathematics Subject Classification ID

Equations involving nonlinear operators (general) (47J05) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

Related Items (14)

Finite dimensional realization of a Tikhonov gradient type-method under weak conditions ⋮ Lavrentiev's regularization method for nonlinear ill-posed equations in Banach spaces ⋮ Modified minimal error method for nonlinear ill-posed problems ⋮ A quadratic convergence yielding iterative method for the implementation of Lavrentiev regularization method for ill-posed equations ⋮ A derivative-free iterative method for nonlinear ill-posed equations with monotone operators ⋮ Projection method for fractional Lavrentiev regularisation method in Hilbert scales ⋮ An apriori parameter choice strategy and a fifth order iterative scheme for Lavrentiev regularization method ⋮ Unnamed Item ⋮ Finite dimensional realization of a quadratic convergence yielding iterative regularization method for ill-posed equations with monotone operators ⋮ A derivative free iterative method for the implementation of Lavrentiev regularization method for ill-posed equations ⋮ Third-order derivative-free methods in Banach spaces for nonlinear ill-posed equations ⋮ Derivative free regularization method for nonlinear ill-posed equations in Hilbert scales ⋮ Extended Newton-type iteration for nonlinear ill-posed equations in Banach space ⋮ Newton-Kantorovich regularization method for nonlinear ill-posed equations involving \(m\)-accretive operators in Banach spaces

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• On the iteratively regularized Gauss-Newton method for solving nonlinear ill-posed problems
• ON APPLICATION OF GENERALIZED DISCREPANCY PRINCIPLE TO ITERATIVE METHODS FOR NONLINEAR ILL-POSED PROBLEMS
• Error estimates of some Newton-type methods for solving nonlinear inverse problems in Hilbert scales
• Regularized Versions of Continuous Newton's Method and Continuous Modified Newton's Method Under General Source Conditions

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