Shifted Kronecker Product Systems

Shifted Kronecker Product Systems

Abstract. A fast method for solving a linear system of the form (A(p) ⊗ · · · ⊗ A(1) − λI)x = b is given where each A(i) is an ni-by-ni matrix. The first step is to convert the problem to triangular form (T (p) ⊗ · · · ⊗ T (1) − λI)y = c by computing the (complex) Schur decompositions of the A(i). This is followed by a recursive back-substitution process that fully exploits the Kronecker struct...

Sparse Solutions to Underdetermined Kronecker Product Systems ∗

Three properties of matrices: the spark, the mutual incoherence and the restricted isometry property have recently been introduced in the context of compressed sensing. We study these properties for matrices that are Kronecker products and show how these properties relate to those of the factors. For the mutual incoherence we also discuss results for sums of Kronecker products.

Kronecker Product of Networked Systems and their Approximates

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...

Block Kronecker Product Graph Model

Since Kronecker Product Graph Model (KPGM) was introduced, it has been widely used to model real networks. The characteristics of the model specially its single fractal structure have made KPGM one of the most important algorithm of the last years. However, the utilization of a single fractal structure decreases the potential of KPGM by limiting the graph space covered by the model. In this pap...

Transformation of the Kronecker Product