A new approach to convergence rate analysis of Tikhonov regularization forparameter identification in heat conduction

In this paper we investigate the stability and convergence rates of the wid ely used output least-squares method with Tikhonov regularization for the i dentification of the conductivity distribution in a heat conduction system. Due to the rather restrictive source conditions and regularity assumptions on the nonlinear parameter-to-solution operator concerned, the existing Ti khonov regularization theory for nonlinear inverse problems is difficult to apply for the convergence rate analysis here. By introducing some new tech niques, we are able to relax these regularity requirements and derive a muc h simpler and easily interpretable source condition but still achieve the s ame convergence rates as the standard Tikhonov regularization theory does.