  Low rank tensor completion is a highly ill-posed inverse problem,
particularly when the data model is not accurate, and some sort of
regularization is required in order to solve it. In this article we focus on
the calibration of the data model. For alternating optimization, we observe
that existing rank adaption methods do not enable a continuous transition
between manifolds of different ranks. We denote this characteristic as
$\textit{instability (under truncation)}$. As a consequence of this property,
arbitrarily small changes in the iterate can have arbitrarily large influence
on the further reconstruction. We therefore introduce a singular value based
regularization to the standard alternating least squares (ALS), which is
motivated by averaging in microsteps. We prove its $\textit{stability}$ and
derive a natural semi-implicit rank adaption strategy. We further prove that
the standard ALS microsteps for completion problems are only stable on
manifolds of fixed ranks, and only around points that have what we define as
$\textit{internal tensor restricted isometry property, iTRIP}$. In conclusion,
numerical experiments are provided that show improvements of the reconstruction
quality up to orders of magnitude in the new Stable ALS Approximation (SALSA)
compared to standard ALS and the well known Riemannian optimization RTTC.
