We describe algorithms for computing maximal determinants of binary circulant matrices of small orders. Here “binary matrix” means a matrix whose elements are drawn from {0, 1} or {−1, 1}. We describe efficient parallel algorithms for the search, using Duval’s algorithm for generation of Lyndon words and the well-known representation of the determinant of a circulant in terms of roots of unity....

In this paper a method is proposed called circulant matching method to approximate the superposition of a number of discrete time batch Markovian arrival sources by a circulant batch Markovian process while matching the stationary cumulative distribution and the autocorrelation sequence of the input rate process Special attention is paid to periodic sources The method is applied to the superpos...

Boundary value methods (BVMs) for ordinary di erential equations require the solution of nonsymmetric, large and sparse linear systems. In this paper, these systems are solved by using the generalized minimal residual (GMRES) method. A block-circulant preconditioner with circulant blocks (BCCB preconditioner) is proposed to speed up the convergence rate of the GMRES method. The BCCB preconditio...

Owing to its orthogonality, simplicity of the inversion and fast algorithms, Jacket transform generalising from the Hadamard transform has played important roles in signal and image processing, mobile communication for coding design, cryptography, etc. In this paper, inspired by the emerging block Jacket transform, a new class of circulant block Jacket matrices (CBJMs) are mathematically define...

The eigenvalue spectrum of a class of nonsymmetric preconditioned matrices arising in time-dependent partial differential equations is analyzed and discussed. The matrices generated by the underlying numerical integrators are small rank perturbations of block Toeplitz matrices; circulant-like preconditioned based on the former are considered. The eigenvalue distribution of the preconditioned ma...

Double-loop and 2-circulant networks are widely used in the design and implementation of local area networks and parallel processing architectures. In this paper, we investigate the routing of a message on circulant networks, that is a key to the performance of this network. We would like to transmit 2k packets from a source node to a destination node simultaneously along paths on G(n; ±s1,±s2,...

A 1-factorisation of a graph G is a decomposition of G into edge-disjoint 1-factors (perfect matchings), and a perfect 1-factorisation is a 1-factorisation in which the union of any two of the 1-factors is a Hamilton cycle. We consider the problem of the existence of perfect 1-factorisations of even order circulant graphs with small degree. In particular, we characterise the 3-regular circulant...

In this paper, we propose a new family of circulant preconditioners for solving ill-conditioned Hermitian Toeplitz systems Ax = b. The eigenval-ues of the preconditioners are given by the convolution products of the generating function f of A with some summation kernels. When f is a nonnegative 2-periodic continuous function deened on ?; ] with a zero of order 2p, we show that the circulant pre...

In the context of computed tomography (CT), iterative image reconstruction techniques are gaining attention because high-quality images are becoming computationally feasible. They involve the solution of large systems of equations, whose cost is dominated by the sparse matrix vector product (SpMV). Our work considers the case of the sparse matrices being block circulant, which arises when takin...

We introduce the class of skew-circulant lattice rules. These are s-dimensional lattice rules that may be generated by the rows of an s×s skewcirculant matrix. (This is a minor variant of the familiar circulant matrix.) We present briefly some of the underlying theory of these matrices and rules. We are particularly interested in finding rules of specified trigonometric degree d. We describe so...