A parameter choice strategy for (iterated) tikhonov regularization of iii-posed problems leading to superconvergence with optimal rates

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 suffices

Keywords:

• Ill-posed problems
• regularization
• superconvergence
• integral equations of the first kind

AMS(MOS):

• 65R20
• 45L10

^*Both authors are on leave from Johannes-Kepler-Universität, Linz, Austria

^*Both authors are on leave from Johannes-Kepler-Universität, Linz, Austria

Notes

^*Both authors are on leave from Johannes-Kepler-Universität, Linz, Austria