let $n,t_1,...,t_k$ be distinct positive integers. a toeplitz graph $g=(v, e)$ denoted by $t_n$ is a graph, where $v ={1,...,n}$ and $e= {(i,j) : |i-j| in {t_1,...,t_k}}$.in this paper, we present some results on decomposition of toeplitz graphs.

In signal and image processing, regularization often requires a rank-revealing decomposition of a symmetric Toeplitz matrix with a small rank deeciency. In this paper, we present an eecient factorization method that exploits symmetry as well as the rank and Toeplitz properties of the given matrix.

A suitable generalization for both the concept of Cayley graphs and that of Toeplitz graphs is given in this note and a number of interesting open problems are proposed. A natural decomposition theorem is obtained for generalized Topelitz graphs and connected generalized Toeplitz graphs. These are new observations and their proofs are direct from the definition.

The classical result of Vandermonde decomposition of positive semidefinite Toeplitz matrices can date back to the early twentieth century. It forms the basis of modern subspace and recent atomic norm methods for frequency estimation. In this paper, we study the Vandermonde decomposition in which the frequencies are restricted to lie in a given interval, referred to as frequency-selective Vander...

The eigenvalue clustering of matrices S−1 n An and C −1 n An is experimentally studied, where An, Sn and Cn respectively are Toeplitz matrices, Strang, and optimal circulant preconditioners generated by the Fourier expansion of a function f(x). Some illustrations are given to show how the clustering depends on the smoothness of f(x) and which preconditioner is preferable. An original technique ...

Toeplitz matrix reconstruction algorithms (TMRAs) are one of the central subroutines in array processing for wireless communication applications. The classical TMRAs have shown excellent accuracy spectral estimation both uncorrelated and coherence sources recent era. However, incorporate eigenvalue decomposition technique estimating eigenvalues Toeplitz-structured covariance matrices that deman...

In this paper, a new algorithm for a high resolution Direction Of Arrival (DOA) estimation method for multiple wideband signals is proposed. The proposed method proceeds in two steps. In the first step, the received signals data is decomposed in a Toeplitz form using the first-order statistics. In the second step, The QR decomposition is applied on the constructed Toeplitz matrix. Compared with...

In the rst part 13] of the paper transformationsmappingToeplitz and Toeplitz-plus-Hankel matrices into generalizedCauchy matrices were studied. In this second part fast algorithms for LU-factorization and inversion of generalized Cauchy matrices are discussed. It is shown that the combinationof transformation pivoting techniques leads to algorithms for indeenite Toeplitz and Toeplitz-plus-Hanke...

When a covariance matrix with a Toeplitz structure is written as the sum of a singular one and a positive scalar multiple of the identity, the singular summand corresponds to the covariance of a purely deterministic component of a time-series whereas the identity corresponds to white noise—this is the Carathéodory-Fejér-Pisarenko (CFP) decomposition. In the present paper we study multivariable ...