Regularized collocation method for Fredholm integral equations of the first kind

DOI10.1016/j.jco.2006.09.002zbMath1131.65113OpenAlexW1975761396MaRDI QIDQ2465282

M. Thamban Nair, Sergei V. Pereverzyev

Publication date: 9 January 2008

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jco.2006.09.002

zbMATH Keywords

collocation methodregularizationill-posed problemsoperator monotone functionsa posteriori parameter choicegeneral source conditionsorder optimal error bounds

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Numerical methods for ill-posed problems for integral equations (65R30) Fredholm integral equations (45B05)

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Cites Work

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• Convergence analysis of a regularized degenerate kernel method for Fredholm integral equations of the first kind
• Convergence rates for regularized solutions of integral equations from discrete noisy data
• Morozov's discrepancy principle under general source conditions
• Convergence analysis of a regularized approximation for solving Fredholm integral equations of the first kind
• Regularization of first kind integral equations with application to Couette viscometry
• Regularization without preliminary knowledge of smoothness and error behaviour
• Regularization of some linear ill-posed problems with discretized random noisy data
• Comparisons of parameter choice methods for regularization with discrete noisy data
• Geometry of linear ill-posed problems in variable Hilbert scales
• Discretization strategy for linear ill-posed problems in variable Hilbert scales
• Regularization of exponentially ill-posed problems
• Morozov's discrepancy principle for tikhonov
• MODULI OF CONTINUITY FOR OPERATOR VALUED FUNCTIONS
• On the Adaptive Selection of the Parameter in Regularization of Ill-Posed Problems
• Convergence rates for Tikhonov regularization from different kinds of smoothness conditions
• Error bounds of discretization methods for boundary integral equations with noisy data
• On the characterization of self-regularization properties of a fully discrete projection method for Symm's integral equation

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