This contribution proposes a decompositional iterative method for the steadystate analysis of Kronecker structured Markov chains [1]. The Markovian system, which is formed by a composition of subsystems using the Kronecker sum operator for local transitions and the Kronecker product operator for synchronized transitions, is assumed to have irreducible subsystem matrices associated with local tr...

The paper presents a system theoretic analysis of network-of-networks which are formed from smaller factor networks via graph Kronecker products. We provide a compositional framework for extending trajectories, stabilizability, controllability and observability of the factor networks to that of the composite network-of-networks. We proceed to delve into the effectiveness of applying these compo...

We propose the tensor Kronecker product singular value decomposition (TKPSVD) that decomposes a real k-way tensor A into a linear combination of tensor Kronecker products with an arbitrary number of d factors A = ∑R j=1 σj A (d) j ⊗ · · · ⊗ A (1) j . We generalize the matrix Kronecker product to tensors such that each factor A j in the TKPSVD is a k-way tensor. The algorithm relies on reshaping...

A new solution technique is proposed for linear systems with large dense matrices of a certain class including those that come from typical integral equations of potential theory. This technique combines Kronecker product approximation and wavelet sparsification for the Kronecker product factors. The user is only required to supply a procedure for computation of each entry of the given matrix. ...

Kronecker-based approaches have been proposed for the solution of structured GSPNs with extremely large state spaces. Representing the transition rate matrix using Kronecker sums and products of smaller matrices virtually eliminates its storage requirements, but introduces various sources of overhead. We show how, by using a new data structure which we call matrix diagrams, we are able to great...

Two new fixed polarity linear Kronecker transforms executed over GF(3) are introduced in this article. Both transforms are based on recursive equations using Kronecker products what allows to obtain simple corresponding fast transforms and very regular butterfly diagrams. The computational costs to calculate the new pair of transforms and their experimental comparison with ternary Reed–Muller t...

A matrix M with nonnegative integer entries is minimal if the nonincreasing sequence of its entries (called π-sequence) is minimal, in the dominance order of partitions, among all nonincreasing sequences of entries of matrices with nonnegative integers that have the same 1-marginals as A. The starting point for this work is an identity that relates the number of minimal matrices that have fixed...

Two new fixed polarity linear Kronecker transforms executed over GF(3) are introduced in this article. Both transforms are based on recursive equations using Kronecker products what allows to obtain simple corresponding fast transforms and very regular butterfly diagrams. The computational costs to calculate the new pair of transforms and their experimental comparison with ternary Reed-Muller t...

The goal of this work is the presentation of some new formats which are useful for the approximation of (large and dense) matrices related to certain classes of functions and nonlocal (integral, integrodifferential) operators, especially for high-dimensional problems. These new formats elaborate on a sum of few terms of Kronecker products of smaller-sized matrices (cf. [37, 38]). In addition to...