In many situations related to acoustics and data communications we are confronted with multiple signals received from a multipath mixture, e.g., the famous cocktail-party problem. A multipath mixture can be described by a mixing matrix, whose elements are the individual transfer functions between a source and a sensor. The mixing matrix is usually unknown, and so are sometimes also the source s...

The main result is the “black dot algorithm” and its fast version for the construction of a new circulant preconditioner for Toeplitz matrices. This new preconditioner C is sought directly as a solution to one of possible settings of the approximation problem A ≈ C + R, where A is a given matrix and R should be a “low-rank” matrix. This very problem is a key to the analysis of superlinear conve...

in this paper, we consider a class of column-weight two quasi-cyclic low-density paritycheck codes in which the girth can be large enough, as an arbitrary multiple of 8. then we devote a convolutional form to these codes, such that their generator matrix can be obtained by elementary row and column operations on the parity-check matrix. finally, we show that the free distance of the convolution...

The energy of a graph was introduced by Gutman in 1978 as the sum of the absolute values of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs. These are Cayley graphs on cyclic groups (i.e. there adjacency matrix is circulant) each of whose eigenvalues is an integer. Given an arbitrary prime power p, we determine all integral circu...

Simulation of multiple-input multiple-output (MIMO) fading channels, with crosscorrelated subchannels, is of paramount importance in performance evaluation of space-time techniques in multiantenna systems. This paper focuses on four methods to simulate several spatio-temporally crosscorrelated stationary complex Gaussian processes: the spectral representation method, the sampling theorem method...

A typical Iranian carbonate matrix block surrounded by an open fracture was modeled in order to understand the fracture-matrix interaction and realize how to model the interaction best. The modeling was carried out by using a fine-scaled Eclipse model in the single porosity mode (the fractures were explicitly modeled). The model was extended to a stack of 6 matrix blocks to understand block-to-...

An important aspect of cryptography with matrices is that given N ×N matrix P over a field F find a class of matrices G over F such that the associated doubly circulant matrix Gc is singular in order that the equation AGB = P in circulant matrices A,B has infinitely many solutions. The aim of this note is to present such a class of matrices G. We also present a direct method of finding the inve...

Circulant matrices can be effective preconditioners for linear systems of equations with a Toeplitz matrix. Several approaches to construct such preconditioners have been described in the literature. This paper focuses on the superoptimal circulant preconditioners proposed by Tyrtyshnikov, and investigates a generalization obtained by allowing generalized circulant matrices. Numerical examples ...

The distance energy of a graph G is a recently developed energy-type invariant, defined as the sum of absolute values of the eigenvalues of the distance matrix of G. There was a vast research for the pairs and families of non-cospectral graphs having equal distance energy, and most of these constructions were based on the join of graphs. A graph is called circulant if it is Cayley graph on the ...

In this paper, based upon the divide-and-conquer strategy, we propose a parallel algorithm for solving the circulant tridiagonal systems, which is simpler than the two previous algorithms proposed by Agui and Jimenez ( 1995) and Chung et al. ( 1995). Our algorithm can be easily generalized to solve the tridiagonal systems, the block-tridiagonal systems, and the circulant block-tridiagonal syste...