This paper considers random (non-Hermitian) circulant matrices, and proves several results analogous to recent theorems on non-Hermitian random matrices with independent entries. In particular, the limiting spectral distribution of a random circulant matrix is shown to be complex normal, and bounds are given for the probability that a circulant sign matrix is singular.

Maximum distance separable (MDS) matrices have applications not only in coding theory but are also of great importance in the design of block ciphers and hash functions. It is highly nontrivial to find MDS matrices which could be used in lightweight cryptography. In a SAC 2004 paper, Junod et. al. constructed a new class of efficient MDS matrices whose submatrices were circulant matrices and th...

We show that a simple geometric result suffices to derive the form of the optimal solution in a large class of finiteand infinite-dimensional maximum entropy problems concerning probability distributions, spectral densities, and covariance matrices. These include Burg’s spectral estimation method and Dempster’s covariance completion, as well as various recent generalizations of the above. We th...

The normal equations constructed by a Toeplitz matrix are studied, in order to nd a suitable preconditioner related to the discrete sine transform. New results are given about the structure of the product of two Toeplitz matrices, which allow the CGN method to achieve a superlinear rate of convergence. This preconditioner outperforms the circulant one for the iterative solution of Toeplitz leas...

Abstract. In the vicinity of extraordinary vertices, the action of a primal subdivision scheme for the construction of arbitrary topology surfaces can be represented by structured matrices that form a hybrid matrix algebra related to the block-circulant algebra. Exploiting the block diagonalization of such matrices, we can easily take into consideration the constraints to be satisfied by their ...

Circulant matrix family occurs in various fields, applied in image processing, communications, signal processing, encoding and preconditioner. Meanwhile, the circulant matrices [1, 2] have been extended in many directions recently. The f(x)-circulant matrix is another natural extension of the research category, please refer to [3, 11]. Recently, some authors researched the circulant type matric...

In this work, we propose an efficient matrix decomposition algorithm for the Method of Fundamental Solutions when applied to three–dimensional boundary value problems governed by elliptic systems of partial differential equations. In particular, we consider problems arising in linear elasticity in axisymmetric domains. The proposed algorithm exploits the block circulant structure of the coeffic...

We prove that standard Gaussian random multipliers are expected to stabilize numerically both Gaussian elimination with no pivoting and block Gaussian elimination and that they also are expected to support the celebrated randomized algorithm for low-rank approximation of a matrix even without customary oversampling. Our tests show similar results where we apply random circulant and Toeplitz mul...

We consider applying the preconditioned conjugate gradient (PCG) method to solve linear systems Ax = b where the matrix A comes from the discretization of second-order elliptic operators. Let (L +)) ?1 (L t +) denote the block Cholesky factorization of A with lower block triangular matrix L and diagonal block matrix. We propose a preconditioner M = (^ L +)) ?1 (^ L t +) with block diagonal matr...

SUMMARY Strang's proposal to use a circulant preconditioner for linear systems of equations with a Hermitian positive definite Toeplitz matrix has given rise to considerable research on circulant preconditioners. This paper presents an {e iϕ }-circulant Strang-type preconditioner.