  This paper is mainly concerned with the inverse scattering problem of
determining the unknown potential for the classical Schr\"odinger equation in
two and three dimensions. We establish the increasing stability of the inverse
scattering problem from either multi-frequency near-field data or
multi-frequency far-field pattern. The stability estimate consists of the
Lipschitz type data discrepancy and the logarithmic high frequency tail of the
potential function, where the latter decreases as the upper bound of the
frequency increases. A novel method is proposed for the proof, which is based
on choosing appropriate incident plane waves and an application of the
quantitative analytic continuation. A key ingredient in the analysis is
employing scattering theory to obtain an analytic region and resolvent
estimates in this region for the resolvent in two and three dimensions. We
further apply this method to study the inverse scattering problem of
determining both the magnetic potential and electric potential for the
three-dimensional magnetic Schr\"odinger equation.
