We consider the iterative solution of linear systems arising from four convection–diffusion model problems: scalar convection–diffusion problem, Stokes problem, Oseen problem and Navier–Stokes problem. We design preconditioners for these model problems that are based on Kronecker product approximations (KPAs). For this we first identify explicit Kronecker product structure of the coefficient ma...

Many very large Markov chains can be modelled e ciently as stochastic automata networks (SANs). A SAN is composed of individual automata which, for the most part, act independently, requiring only infrequent interaction. SANs represent the generator matrix Q of the underlying Markov chain compactly as the sum of Kronecker products of smaller matrices. Thus, storage savings are immediate. The be...

Weichsel (Proc. Amer. Math. Soc. 13 (1962), 47-52) proved that the Kronecker product of two connected bipartite graphs consists of two connected components. A condition on the factor graphs is presented which ensures that such components are isomorphic. It is demonstrated that several familiar and easily constructible graphs are amenable to that condition. A partial converse is proved for the a...

In this paper, we propose a differential space-time modulation (DSTM) scheme for multiple input multiple output (MIMO) systems with 2, 4, and 8 transmit antennas. This scheme is used for MIMO systems where the channel coefficients are not available at both the transmitter and the receiver. For 2 transmit antennas, the transmission matrices are selected from Weyl group. We use the Kronecker prod...

Image restoration applications often result in ill-posed least squares problems involving large, structured matrices. One approach used extensively is to restore the image in the frequency domain, thus providing fast algorithms using ffts. This is equivalent to using a circulant approximation to a given matrix. Iterative methods may also be used eeectively by exploiting the structure of the mat...

Entangled quantum states are an important component of quantum computing techniques such as quantum error-correction, dense coding and quantum teleportation. We determine the requirements for a state in the Hilbert space C C for N to be entangled and a solution to the corresponding “factorization” problem if this is not the case. We consider the implications of these criteria for computer algeb...

We provide a set of maximal rank-deficient submatrices of a Kronecker product of two matrices A ⊗ B, and in particular the Kronecker product of Fourier matrices F = Fn1 ⊗ . . . ⊗ Fnk . We show how in the latter case, maximal rank-deficient submatrices can be constructedas tilings of rank-one blocks. Such tilings exist for any subgroup of a suitable Abelian group associated to the matrix F . The...

This paper introduces a new transform known as HARWHT. It results from the Kronecker product of the discrete Hartley transform (DHT) and discrete Walsh-Hadamard transform (WHT). The eigenvectors and eigenvalues of the HARWHT transform matrices are presented using Kronecker product. Then, the results of the eigen decomposition of the transform matrices are used to define discrete fractional HARW...