Abstract. Research on preconditioning Toeplitz matrices with circulant matrices has been active recently. The preconditioning technique can be easily generalized to block Toeplitz matrices. That is, for a block Toeplitz matrix T consisting of N N blocks with M M elements per block, a block circulant matrix R is used with the same block structure as its preconditioner. In this research, the spec...

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...

We study the Smith forms of matrices form f ( C g ) where t , ∈ R [ ] is an elementary divisor domain and companion matrix (monic) polynomial . Prominent examples such are circulant matrices, skew-circulant triangular Toeplitz matrices. In particular, we reduce calculation to that F G quotients by some common divisor. This allows us express last non-zero determinantal as a resultant. A key tool...

We study the polynomial Φ(x, y) = ∏p−1 j=0 ( 1− xω − yω ) , where ω is a primitive pth root of unity. This polynomial arises in CR geometry [1]. We show that it is the determinant of the p× p circulant matrix whose first row is (1,−x, 0, . . . , 0,−y, 0, . . . ,0), the −y being in position q + 1. Therefore, the coefficients of this polynomial Φ are integers that count certain classes of permuta...

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...

the main aim of this paper is to introduce three classes $h^0_{p,q}$, $h^1_{p,q}$ and $th^*_p$ of $p$-harmonic mappings and discuss the properties of mappings in these classes. first, we discuss the starlikeness and convexity of mappings in $h^0_{p,q}$ and $h^1_{p,q}$. then establish the covering theorem for mappings in $h^1_{p,q}$. finally, we determine the extreme points of the class $th^*_{p}$.

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 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...