The numerical solution of large and sparse nonsymmetric linear systems of algebraic equations is usually the most time consuming part of time-step integrators for differential equations based on implicit formulas. Preconditioned Krylov subspace methods using Strang block circulant preconditioners have been employed to solve such linear systems. However, it has been observed that these block cir...

In this paper, A-factor circulant matrices with the structure of a circulant, but with the entries below the diagonal multiplied by the same factor A are introduced. Then the generalized rotation and hyperbolic matrices are defined, using an idea due to Ungar. Considering the exponential property of the generalized rotation and hyperbolic matrices, additive formulae for corresponding matrices a...

A framework for constructing circulant and block circulant preconditioners (C) for a symmetric linear system Ax= b arising from signal and image processing applications is presented in this paper. The proposed scheme does not make explicit use of matrix elements of A. It is ideal for applications in which A only exists in the form of a matrix vector multiplication routine, and in which the proc...

A class of maximum-girth geometrically structured quasi-cyclic (QC) low-density parity-check (LDPC) codes with columnweight J 3 is presented. The method is based on the slope concept between two circulant permutation matrices and the concept of slope matrices. A LDPC code presented by a mv ×ml parity-check matrix H , consisting of m ×m matrices each of which is either a circulant permutation ma...

A multilevel circulant is defined as a graph whose adjacency matrix has a certain block decomposition into circulant matrices. A general algebraic method for finding the eigenvectors and the eigenvalues of multilevel circulants is given. Several classes of graphs, including regular polyhedra, suns, and cylinders can be analyzed using this scheme.

In this paper we present a method to search q circulant matrices; the concatenation of these circulant matrices with circulant identity matrix generates quasi-cyclic codes with high various code rate q/(q+1) (q an integer). This method searches circulant matrices in order to find the good quasi-cyclic code (QCC) having the largest minimum distance. A modified simulated annealing algorithm is us...

In this paper we consider numerical solution of 3D linear elasticity equations described by a coupled system of second order elliptic partial differential equations. This system is discretized by trilinear parallelepipedal finite elements. Preconditioned Conjugate Gradient iterative method is used for solving large-scale linear algebraic systems arising after the Finite Element Method (FEM) dis...

In this paper we consider numerical solution of 3D linear elasticity equations described by a coupled system of second order elliptic partial differential equations. This system is discretized by trilinear parallelepipedal finite elements. Preconditioned Conjugate Gradient iterative method is used for solving large-scale linear algebraic systems arising after the Finite Element Method (FEM) dis...

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...

This paper proposes a new, large diffusion layer for the AES block cipher. This new layer replaces the ShiftRows and MixColumns operations by a new involutory matrix in every round. The objective is to provide complete diffusion in a single round, thus sharply improving the overall cipher security. Moreover, the new matrix elements have low Hamming-weight in order to provide equally good perfor...