The Kronecker product and stochastic automata networks

The Kronecker Product and Stochastic Automata Networks

This paper can be thought of as a companion paper to Van Loan’s The Ubiquitous Kronecker Product paper [23]. We collect and catalog the most useful properties of the Kronecker product and present them in one place. We prove several new properties that we discovered in our search for a Stochastic Automata Network preconditioner. We conclude by describing one application of the Kronecker product,...

Testing the Nearest Kronecker Product Preconditioner on Markov Chains and Stochastic Automata Networks

T paper is the experimental follow-up to Langville and Stewart (2002), where the theoretical background for the nearest Kronecker product (NKP) preconditioner was developed. Here we test the NKP preconditioner on both Markov chains (MCs) and stochastic automata networks (SANs). We conclude that the NKP preconditioner is not appropriate for general MCs, but is very effective for a MC stored as a...

Vertex Censored Stochastic Kronecker Product Graphs

Stochastic Kronecker Product Graphs are an interesting and useful class of Generative Network Models. They can be fitted using a fast Maximum Likelihood Estimator and reproduce many important statistical properties commonly found in large real-world networks. However, they suffer from an unfortunate drawback: the need to pad the Stochastic Kronecker Product Graph with isolated vertices. To addr...

Optimizing Tensor Product Computations in Stochastic Automata Networks

In this paper we consider some numerical issues in computing solutions to networks of stochastic automata (SAN). In particular our concern is with keeping the amount of computation per iteration to a minimum, since iterative methods appear to be the most eeective in determining numerical solutions. In a previous paper we presented complexity results concerning the vector-descriptor multiplicati...

Stochastic Automata Networks