Solving the Backward Heat Conduction Problem by Data Fitting with Multiple Regularizing Parameters

Abstract

We propose a new reconstruction scheme for the backward heat conduction problem. By using the eigenfunction expansions, this ill-posed problem is solved by an optimization problem, which is essentially a regularizing scheme for the noisy input data with both the number of truncation terms and the approximation accuracy for the final data as multiple regularizing parameters. The convergence rate analysis depending on the strategy of choosing regularizing parameters as well as the computational accuracy of eigenfunctions is given. Numerical implementations are presented to show the validity of this new scheme.