Asymptotic L∞-based comparison of Tikhonov regularization and Landweber iteration

AbstractThe distance between the Tikhonov and Landweber regularized solutions of a linear inverse problem is partly controlled by the L∞-norm of the difference in their corresponding singular value filters. For large Landweber iteration number, the regularization parameter of the closest Tikhonov filter to a given Landweber filter is determined. This asymptotically computed parameter compares well with the numerically computed value even for moderate sized iteration number. A consequence of the analysis is to determine the range of singular values to which the difference in regularized solutions is most sensitive