Padé iteration method for regularization

In this study we present iterative regularization methods using rational approximations, in particular, Padé approximants, which work well for ill-posed problems. We prove that the (k, j)-Padé method is a convergent and order optimal iterative regularization method in using the discrepancy principle of Morozov. Furthermore, we present a hybrid Padé method, compare it with other well-known methods and found that it is faster than the Landweber method. It is worth mentioning that this study is a completion of the paper [A. Kirsche, C. Böckmann, Rational approximations for ill-conditioned equation systems, Appl. Math. Comput. 171 (2005) 385-397] where this method was treated to solve ill-conditioned equation systems.