ON RULES FOR STOPPING THE CONJUGATE GRADIENT TYPE METHODS IN ILL‐POSED PROBLEMS

DOI10.3846/1392-6292.2007.12.61-70zbMath1121.65059OpenAlexW2072753965MaRDI QIDQ3594295

Reimo Palm, Uno Hämarik

Publication date: 7 August 2007

Published in: Mathematical Modelling and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3846/1392-6292.2007.12.61-70

zbMATH Keywords

numerical examplesHilbert spacesdiscrepancy principlelinear ill-posed problemsstopping rulelinear bounded operatornoise levelmonotone error rule\(L\)-curve ruleconjugate gradient type iteration methods

Mathematics Subject Classification ID

Numerical solutions to equations with linear operators (65J10) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52)

Related Items (7)

Inverse problems for a parabolic integrodifferential equation in a convolutional weak form ⋮ Weighted conjugate gradient-type methods for solving quadrature discretization of Fredholm integral equations of the first kind ⋮ Comparison of parameter choices in regularization algorithms in case of different information about noise level ⋮ On Minimization Strategies for Choice of the Regularization Parameter in Ill-Posed Problems ⋮ An iterative method to compute minimum norm solutions of ill-posed problems in Hilbert spaces ⋮ Monotonicity of error of regularized solution and its use for parameter choice ⋮ Fourier reconstruction for diffraction tomography of an object rotated into arbitrary orientations

Uses Software

• Regularization tools

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