  This paper is a close follow-up of Kaltenbacher and Tomba 2013 and Jin 2012,
where Newton-Landweber iterations have been shown to converge either
(unconditionally) without rates or (under an additional regularity assumption)
with rates. The choice of the parameters in the method were different in each
of these two cases. We now found a unified and more general strategy for
choosing these parameters that enables both convergence and convergence rates.
Moreover, as opposed to the previous one, this choice yields strong convergence
as the noise level tends to zero, also in the case of no additional regularity.
Additionally, the resulting method appears to be more efficient than the one
from Kaltenbacher and Tomba 2013, as our numerical tests show.
