In many applications, e.g. digital signal processing, discrete inverse scattering, linear prediction etc., Toeplitz-plus-Hankel (T + H) matrices need to be inverted. (For further applications see [1] and references therein). Firstly the T +H matrix inversion problem has been solved in [2] where it was reduced to the inversion problem of the block Toeplitz matrix (the so-called mosaic matrix). T...

We discuss formal orthogonal polynomials with respect to a moment matrix that has no structure whatsoever. In the classical case the moment matrix is often a Hankel or a Toeplitz matrix. We link this to block factorization of the moment matrix and its inverse, the block Hessenberg matrix of the recurrence relation, the computation of successive Schur complements and general subspace iterative m...

A block Toeplitz algorithm is proposed to perform the J-spectral factorization of a para-Hermitian polynomial matrix. The input matrix can be singular or indefinite, and it can have zeros along the imaginary axis. The key assumption is that the finite zeros of the input polynomial matrix are given as input data. The algorithm is based on numerically reliable operations only, namely computation ...

In this paper we study the effect of block diagonalization of a nearly diagonal matrix by iterating the related Riccati equations. We show that the iteration is fast, if a matrix is diagonally dominant or scaled diagonally dominant and the block partition follows an appropriately defined spectral gap. We also show that both kinds of diagonal dominance are not destroyed after the block diagonali...

A special structure of a kind of matrices, r−block monomial and r−block diagonal matrices, is introduced. Theirs nonnegative Drazin inverses have been studied. The influence of these matrices on the positiveness of the trajectory of a descriptor system has been analyzed. Key–Words:Drazin inverse, nonnegative matrix, block monomial matrix, descriptor system.

In this paper, necessary and sufficient conditions are given for the k-regularity of block fuzzy matrices in terms of the schur complements of its k-regular diagonal blocks. A formula for k-g-inverse of a block fuzzy matrix is established. A set of conditions for a block matrix to be expressed as the sum of k-regular block matrices is obtained. Mathematics Subject Classification: 15B15; 15A09

Estimation of large covariance matrices has drawn considerable recent attention, and the theoretical focus so far has mainly been on developing a minimax theory over a fixed parameter space. In this paper, we consider adaptive covariance matrix estimation where the goal is to construct a single procedure which is minimax rate optimal simultaneously over each parameter space in a large collectio...

To analyze the limiting spectral distribution of some random blockmatrices, Girko [7] uses a system of canonical equations from [6]. In this paper, we use the method of moments to give an integral form for the almost sure limiting spectral distribution of such matrices.

We characterize the pseudo-equivalence of a block lower triangular matrix T = [Tij ] over a regular ring, and its block diagonal matrix D(T ) = [Tii], in terms of suitable Roth consistency conditions. The latter can in turn be expressed in terms of the solvability of certain matrix equations of the form TiiX − Y Tjj = Uij .

We present some observations on the block triangular form (btf) of structurally symmetric, square, sparse matrices. If the matrix is structurally rank deficient, its canonical btf has at least one underdetermined and one overdetermined block. We prove that these blocks are transposes of each other. We further prove that the square block of the canonical btf, if present, has a special fine struc...