The trade-off between regularity and stability in Tikhonov regularization

DOI10.1090/S0025-5718-97-00811-9zbMath0854.65123OpenAlexW1975802113MaRDI QIDQ5691007

Markus Hegland, Robert S. Anderssen, M. Thamban Nair

Publication date: 9 January 1997

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-97-00811-9

zbMATH Keywords

numerical exampleconvergence rateTikhonov regularizationill-posed operator equationsbest-possible worst-error estimatestrade-off between stabilization and regularity

Mathematics Subject Classification ID

Numerical methods for ill-posed problems for integral equations (65R30) Fredholm integral equations (45B05) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

Related Items (9)

Role of Hilbert Scales in Regularization Theory ⋮ Error bounds and parameter choice strategies for simplified regularization in Hilbert scales ⋮ A numerical study of inverse heat conduction problems ⋮ A three-step algorithm for solving 2D inverse magnetostatic problems for magnetron design applications ⋮ Regularization of ill-posed operator equations: an overview ⋮ On Morozov's method for Tikhonov regularization as an optimal order yielding algorithm ⋮ A shape optimization problem constrained with the Stokes equations to address maximization of vortices ⋮ A unified treatment for Tikhonov regularization using a general stabilizing operator ⋮ Optimal order results for a class of regularization methods using unbounded operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Parameter choice by discrepancy principles for the approximate solution of ill-posed problems
• Parameter choice by discrepancy principles for ill-posed problems leading to optimal convergence rates
• A generalization of Arcangeli's method for ill-posed problems leading to optimal rates
• Pitfalls in the Numerical Solution of Linear Ill-Posed Problems
• A Method for Solving Ill-Posed Linear Operator Equations
• An a Posteriori Parameter Choice for Tikhonov Regularization in Hilbert Scales Leading to Optimal Convergence Rates
• A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
• Regularization with Differential Operators. II: Weak Least Squares Finite Element Solutions to First Kind Integral Equations
• An Optimal Order Regularization Method which Does Not Use Additional Smoothness Assumptions
• Error bounds for tikhonov regularization in hilbert scales
• SCALES OF BANACH SPACES
• On the asymptotic order of accuracy of Tikhonov regularization

This page was built for publication: The trade-off between regularity and stability in Tikhonov regularization