In this paper, fast algorithms for solving RFPrLR circulant linear systems are presented by the fast algorithm for computing polynomials. The unique solution is obtained when the RFPrLR circulant matrix over the complex field C is nonsingular, and the special solution and general solution are obtained when the RFPrLR circulant matrix over the complex field C is singular. The extended algorithms...

The variety of quasigroups satisfying the identity (xy)(zy) = xz mirrors the variety of groups, and offers a new look at groups and their multiplication tables. Such quasigroups are constructed from a group using right division instead of multiplication. Their multiplication tables consist of circulant blocks which have additional symmetries and have a concise presentation. These tables are a r...

for a symmetric group $g:=sym(n)$ and a conjugacy class $mathcal{x}$ of involutions in $g$, it is known that if the class of involutions does not have a unique fixed point, then - with a few small exceptions - given two elements $a,x in mathcal{x}$, either $angbrac{a,x}$ is isomorphic to the dihedral group $d_{8}$, or there is a further element $y in mathcal{x}$ such that $angbrac{a,y} cong ang...

In signal acquisition, Toeplitz and circulant matrices are widely used as sensing operators. They correspond to discrete convolutions and are easily or even naturally realized in various applications. For compressive sensing, recent work has used random Toeplitz and circulant sensing matrices and proved their efficiency in theory, by computer simulations, as well as through physical optical exp...

The present monograph studies the asymptotic behaviour of eigenvalues, products and functions of block Toeplitz matrices generated by the Fourier coefficients of a continuous matrix-valued function. This study is based on the concept of asymptotically equivalent sequences of non-square matrices. The asymptotic results on block Toeplitz matrices obtained are applied to vector asymptotically wide...

Third generation mobile radio systems will employ TD-CDMA in their TDD mode. In a TD-CDMA mobile radio system, jointdetection is equivalent to solving a least squares problem with a block-Toeplitz system matrix. By extending this matrix to a block-circulant matrix, it is possible to blockdiagonalize the matrix with Fast Fourier Transforms. For the typical system scenario of a TD-CDMA system, th...

An equitable vertex coloring for the splitting of block circulant graphs is investigated. The comprises matrices, where each itself a matrix. These blocks in row are cyclically shifted one place to right from those previous row. We approached such matrix representation and derived their independent sets using neighbourhoods vertex. This classification makes process be simpler most cases. In thi...

Introduced the notion of symmetric circulant matrix on skew field, an easy method is given to determine the inverse of symmetric circulant matrix on skew field , with this method , we derived the formula of determine inverse about several special type of symmetric circulant matrix. Mathematics Subject Classification: 05A19, 15A15

In this paper we present a time-polynomial recognition algorithm for circulant graphs of prime order. A circulant graphG of order n is a Cayley graph over the cyclic groupZn: Equivalently, G is circulant i its vertices can be ordered such that the corresponding adjacency matrix becomes a circulant matrix. To each circulant graph we may associate a coherent con guration A and, in particular, a S...

In this paper, we discuss the solutions to a class of Hermitian positive deenite system Ax = b by the preconditioned conjugate gradient method with circulant preconditioner C. In general, the smaller the condition number (C ?1=2 AC ?1=2) is, the faster the convergence of the method will be. The circulant matrix C b that minimizes (C ?1=2 AC ?1=2) is called the best conditioned circulant precond...