A parameter choice strategy for (iterated) tikhonov regularization of iii-posed problems leading to superconvergence with optimal rates
Authors:
- 1 January 1988
- journal article
- research article
- Published by Taylor & Francis in Applicable Analysis
- Vol. 27 (1-3) , 5-18
Abstract
For ordinary and iterated Tikhonov regularization of linear ill-posed problems, we propose a parameter choice strategy that leads to optimal (super-) convergence rates for certain linear functionals of the regularized solution. It is not necessary to know the smoothness index of the exact solution; approximate knowledge of the smoothness index for the linear functional sufficesKeywords
This publication has 8 references indexed in Scilit:
- An a Posteriori Parameter Choice for Tikhonov Regularization in Hilbert Scales Leading to Optimal Convergence RatesSIAM Journal on Numerical Analysis, 1988
- On the choice of the regularization parameter for iterated Tikhonov regularization of III-posed problemsJournal of Approximation Theory, 1987
- OPTIMAL PARAMETER CHOICE FOR ORDINARY AND ITERATED TIKHONOV REGULARIZATION1987
- The Linear Functional Strategy for Improperly Posed Problems1986
- Approximate Solution of Ill-Posed Equations: Arbitrarily Slow Convergence vs. Superconvergence1985
- Methods for Solving Incorrectly Posed Problems1984
- Necessary and sufficient conditions for convergence of regularization methods for solving linear operator equations of the first kindNumerical Functional Analysis and Optimization, 1981
- On the Use of Linear Functionals for Abel—Type Integral Equations in Applications1980