Approximation of the Tikhonov regularization parameter through Aitken's extrapolation

DOI10.1016/j.apnum.2023.04.008zbMath1523.65038OpenAlexW4368364881MaRDI QIDQ6169242

Paraskevi Fika

Publication date: 11 July 2023

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2023.04.008

zbMATH Keywords

Tikhonov regularizationMorozov's discrepancy principlegeneralized cross-validationquasi-optimality criterionAitken's extrapolationGfrerer/Raus method

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Numerical optimization and variational techniques (65K10)

Cites Work

• Comparison of parameter choices in regularization algorithms in case of different information about noise level
• Comparing parameter choice methods for regularization of ill-posed problems
• Error estimates for the regularization of least squares problems
• Error estimates for large-scale ill-posed problems
• Prediction properties of some extrapolation methods
• Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross-validation
• Estimates for the generalized cross-validation function via an extrapolation and statistical approach
• GCV for Tikhonov regularization by partial SVD
• Old and new parameter choice rules for discrete ill-posed problems
• The application of regularisation to variable selection in statistical modelling
• Conditional gradient Tikhonov method for a convex optimization problem in image restoration
• On Krylov projection methods and Tikhonov regularization
• Aitken's method for estimating bilinear forms arising in applications
• Regularization tools version \(4.0\) for matlab \(7.3\)
• Global Golub-Kahan bidiagonalization applied to large discrete ill-posed problems
• GCV for Tikhonov regularization via global Golub–Kahan decomposition
• An Introduction to the Mathematical Theory of Inverse Problems
• A Stochastic Estimator of the Trace of the Influence Matrix for Laplacian Smoothing Splines
• An A Posteriori Parameter Choice for Ordinary and Iterated Tikhonov Regularization of Ill-Posed Problems Leading to Optimal Convergence Rates
• A General Heuristic for Choosing the Regularization Parameter in Ill-Posed Problems
• Stochastic estimates for the trace of functions of matrices via Hadamard matrices
• On the block Lanczos and block Golub–Kahan reduction methods applied to discrete ill‐posed problems
• On the Lanczos and Golub–Kahan reduction methods applied to discrete ill‐posed problems
• Matrix theory. Basic results and techniques
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Approximation of the Tikhonov regularization parameter through Aitken's extrapolation