Matrices that are sum of Kronecker products arise in
many applications such as graph analysis, image processing, queueing theory,
and most notably numerical analysis, in the discretization
of PDEs with separable coefficients.

We discuss computational strategies that exploit this structure to
efficiently solve associated linear equations. Moreover,
we investigate sparsity and pattern properties of functions of these matrices,
which can be exploited in, e.g., the design of adaptive
spectral/hp discretizations of elliptic boundary-value problems.

This is partially joint work with Michele Benzi (Emory University, USA),
and also with Claudio Canuto (Politecnico di Torino, I) and Marco Verani
(Politecnico di Milano, I).