  The Nystr\"om method offers an effective way to obtain low-rank approximation
of SPD matrices, and has been recently extended and analyzed to nonsymmetric
matrices (leading to the generalized Nystr\"om method). It is a randomized,
single-pass, streamable, cost-effective, and accurate alternative to the
randomized SVD, and it facilitates the computation of several matrix low-rank
factorizations.
  In this paper, we take these advancements a step further by introducing a
higher-order variant of Nystr\"om's methodology tailored to approximating
low-rank tensors in the Tucker format: the multilinear Nystr\"om technique. We
show that, by introducing appropriate small modifications in the formulation of
the higher-order method, strong stability properties can be obtained. This
algorithm retains the key attributes of the generalized Nystr\"om method,
positioning it as a viable substitute for the randomized higher-order SVD
algorithm.
