Matrices with Kronecker sum structure arise in many applications involving discretized partial differential equations, when the domain is a rectangle or a parallelepiped, and certain discretization strategies are employed. Other applications include image processing, queueing theory, graph analysis, and network design.
We present new sharp decay bounds for a broad class of Hermitian matrix functions where the matrix argument is the Kronecker sum of banded matrices. For a large matrix function times a vector, we also derive a computational strategy that significantly lowers the memory requirements and computational efforts of the standard approximations.
All our findings are illustrated by numerical experiments with typical functions used in applications.
Joint work with Michele Benzi, Emory University, USA.