Regularized Versions of Continuous Newton's Method and Continuous Modified Newton's Method Under General Source Conditions

DOI10.1080/01630560802484294zbMath1155.65043OpenAlexW2088812970MaRDI QIDQ5302574

P. Ravishankar, M. Thamban Nair

Publication date: 7 January 2009

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630560802484294

zbMATH Keywords

regularizationstopping rulesource conditionscontinuous Newton's methodnonlinear ill-posed equation

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Nonlinear ill-posed problems (47J06) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical solution to inverse problems in abstract spaces (65J22) Dynamical systems methods for problems in mechanics (70G60)

Related Items (12)

Multilevel augmentation methods for nonlinear ill-posed problems ⋮ A quadratic convergence yielding iterative method for the implementation of Lavrentiev regularization method for ill-posed equations ⋮ An analysis of Lavrentiev regularization method and Newton type process for nonlinear ill-posed problems ⋮ Cubic convergence order yielding iterative regularization methods for ill-posed Hammerstein type operator equations ⋮ An apriori parameter choice strategy and a fifth order iterative scheme for Lavrentiev regularization method ⋮ Two-step modified Newton method for nonlinear Lavrentiev regularization ⋮ Two-step Newton-Tikhonov method for Hammerstein-type equations: finite-dimensional realization ⋮ A generalization of continuous regularized Gauss–Newton method for ill-posed problems ⋮ Unnamed Item ⋮ Regularization of ill-posed operator equations: an overview ⋮ Expanding the applicability of an a posteriori parameter choice strategy for Tikhonov regularization of nonlinear ill-posed problems ⋮ Expanding the applicability of an iterative regularization method for ill-posed problems

Cites Work

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• A convergence analysis of the Landweber iteration for nonlinear ill-posed problems
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• Continuous modified Newton's-type method for nonlinear operator equations
• A level set method for inverse problems
• A convergence analysis of iterative methods for the solution of nonlinear ill-posed problems under affinely invariant conditions
• On broyden's method for the regularization of nonlinear ill-posed problems
• On the asymptotical regularization of nonlinear ill-posed problems
• On the method of Lavrentiev regularization for nonlinear ill-posed problems
• Convergence rates of the continuous regularized Gauss—Newton method

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