Multipreconditioned GMRES for simulating stochastic automata networks

Multipreconditioned Gmres for Shifted Systems

An implementation of GMRES with multiple preconditioners (MPGMRES) is proposed for solving shifted linear systems with shift-and-invert preconditioners. With this type of preconditioner, the Krylov subspace can be built without requiring the matrix-vector product with the shifted matrix. Furthermore, the multipreconditioned search space is shown to grow only linearly with the number of precondi...

Preconditioning for Stochastic Automata Networks

LANGVILLE, AMY N. Preconditioning for Stochastic Automata Networks. (Under the direction of William J. Stewart.) Many very large Markov chains can be modeled efficiently as Stochastic Automata Networks (SANs). A SAN is composed of individual automata that, for the most part, act independently, requiring only infrequent interaction. SANs represent the generator matrix Q of the underlying Markov ...

Stochastic Automata Networks

Quantum Recurrent Networks for Simulating Stochastic Processes

We introduce the concept of quantum recurrent networks by incorporating classical feedback loops into conventional quantum networks. We show that the dynamical evolution of such networks, which interleave quantum evolution with measurement and reset operations, exhibit novel dynamical properties finding application in pattern recognition, optimization and simulation. Moreover, decoherence in qu...

Circulant preconditioners for stochastic automata networks

Stochastic Automata Networks (SANs) are widely used in modeling communication systems , manufacturing systems and computer systems. The solution of the steady state distribution cannot be obtained eeciently by direct methods such as LU decomposition due to the huge size of the generator matrix. EEcient numerical algorithm should make use of the tensor structure of SANs' generator matrix. The ge...