A convergence analysis of iterative methods for the solution of nonlinear ill-posed problems under affinely invariant conditions
From MaRDI portal
Publication:4218594
DOI10.1088/0266-5611/14/5/002zbMath0915.65053OpenAlexW2012551465MaRDI QIDQ4218594
Peter Deuflhard, Heinz W. Engl, Otmar Scherzer
Publication date: 16 June 1999
Published in: Inverse Problems (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1088/0266-5611/14/5/002
convergenceiterative methodsnonlinear ill-posed problemsaffine invarianceLandweber methodGauss-Newton methods
Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)
Related Items
A comparison of the Landweber method and the Gauss--Newton method for an inverse parabolic boundary value problem ⋮ Natural linearization for the identification of nonlinear heat transfer laws ⋮ Towards a general convergence theory for inexact Newton regularizations ⋮ Regularized Versions of Continuous Newton's Method and Continuous Modified Newton's Method Under General Source Conditions ⋮ 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 ⋮ Huygens' principle and iterative methods in inverse obstacle scattering ⋮ Analysis of a heuristic rule for the IRGNM in Banach spaces with convex regularization terms ⋮ On the order optimality of the regularization via inexact Newton iterations ⋮ Two-step modified Newton method for nonlinear Lavrentiev regularization ⋮ Convergence of the Hilbert uniqueness method via Tikhonov regularization ⋮ Analysis of the iteratively regularized Gauss–Newton method under a heuristic rule ⋮ Newton-type methods and their modifications for inverse heat conduction problems ⋮ Fast fully iterative Newton-type methods for inverse problems ⋮ Convergence analysis of an inexact iteratively regularized Gauss-Newton method under general source conditions ⋮ Logarithmic convergence rate of Levenberg–Marquardt method with application to an inverse potential problem ⋮ A generalization of continuous regularized Gauss–Newton method for ill-posed problems ⋮ Iteratively regularized Gauss-Newton method for atmospheric remote sensing ⋮ Iteratively regularized Gauss-Newton method for bound-constraint problems in atmospheric remote sensing ⋮ Regularization by projection: Approximation theoretic aspects and distance functions ⋮ Unnamed Item ⋮ Iteratively regularized gradient method with a posteriori stopping rule for 2D inverse gravimetry problem ⋮ A MANN ITERATIVE REGULARIZATION METHOD FOR ELLIPTIC CAUCHY PROBLEMS ⋮ A family of preconditioned iteratively regularized methods for nonlinear minimization ⋮ Iterative Solution Methods ⋮ A mixed Newton-Tikhonov method for nonlinear ill-posed problems ⋮ A second order Newton method for sound soft inverse obstacle scattering ⋮ On the discrepancy principle for some Newton type methods for solving nonlinear inverse problems ⋮ Toward Global Convergence for Strongly Nonlinear Ill-Posed Problems via a Regularizing Multilevel Approach ⋮ Expanding the applicability of an iterative regularization method for ill-posed problems ⋮ Numerical differentiation from a viewpoint of regularization theory ⋮ A Recursive Algorithm for MultiFrequency Acoustic Inverse Source Problems ⋮ Regularization of exponentially ill-posed problems ⋮ Parallel iteratively regularized Gauss–Newton method for systems of nonlinear ill-posed equations
