  For solving linear ill-posed problems regularization methods are required
when the right hand side is with some noise. In the present paper regularized
solutions are obtained by implicit iteration methods in Hilbert scales. % By
exploiting operator monotonicity of certain functions and interpolation
techniques in variable Hilbert scales, we study these methods under general
smoothness conditions. Order optimal error bounds are given in case the
regularization parameter is chosen either {\it a priori} or {\it a posteriori}
by the discrepancy principle. For realizing the discrepancy principle, some
fast algorithm is proposed which is based on Newton's method applied to some
properly transformed equations.
