In this paper, a so-called auxiliary matrix polynomial Xn(z) and a true right formal orthogonal matrix polynomial (FOMP) A 1 n (z) is connected to each well-conditioned leading principal block submatrix of a given block Toeplitz matrix. From these two matrix polynomi-als, all other right FOMPs of block n of a system of block biorthogonal matrix polynomials with respect to the block Toeplitz mom...

In this paper we deal with a single-antenna discrete-time flat-fading channel. The fading process is assumed to be stationary for the duration of a single data block. From block to block the fading process is allowed to be non-stationary. The number of scatterers bounds the rank of the channels covariance matrix. The signal-to-noise ratio (SNR), the user velocity, and the data block-length defi...

Block coherence of matrices plays an important role in analyzing the performance of block compressed sensing recovery algorithms (Bajwa and Mixon, 2012). In this paper, we characterize two block coherence metrics: worstcase and average block coherence. First, we present lower bounds on worst-case block coherence, in both the general case and also when the matrix is constrained to be a union of ...

lsmr (least squares minimal residual) is an iterative method for the solution of the linear system of equations and leastsquares problems. this paper presents a block version of the lsmr algorithm for solving linear systems with multiple right-hand sides. the new algorithm is based on the block bidiagonalization and derived by minimizing the frobenius norm of the resid ual matrix of normal equa...

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...

For MinRes and SymmLQ it is essential to compute a QR decomposition of a tridiagonal coefficient matrix gained in the Lanczos process. This QR decomposition is constructed by an update scheme applying in every step a single Givens rotation. Using complex Householder reflections we generalize this idea to block tridiagonal matrices that occur in generalizations of MinRes and SymmLQ to block meth...

A small portable network forensic evidence collection device is presented which is built using inexpensive embedded hardware and open source software. The device o ers several modes of operation for di erent live network evidence collection scenarios involving single network nodes. This includes the use of promiscuous packet capturing to enhance evidence collection from remote network sources, ...

This paper introduces packet-oriented block codes for the recovery of lost packets and the correction of an erroneous single packet. Specifically, a family of systematic codes is proposed, based on a Vandermonde matrix applied to a group of k information packets to construct r redundant packets, where the elements of the Vandermonde matrix are bit-level right arithmetic shift operators. The cod...

Let an n x -matrix A have m < (m ? 2) different eigenvalues ?j of the algebraic multiplicity (j = 1,..., m). It is proved that there are ?j-matrices Aj, each which has a unique eigenvalue ?j, such similar to block-diagonal matrix ?D diag (A1,A2,..., Am). I.e. invertible T, T-1AT ?D. Besides, sharp bound for number kT := ||T||||T-1|| derived. As applications these results we obtain norm estim...

In this paper, block distance matrices are introduced. Suppose F is a square block matrix in which each block is a symmetric matrix of some given order. If F is positive semidefinite, the block distance matrix D is defined as a matrix whose (i, j)-block is given by D ij = F ii +F jj −2F ij. When each block in F is 1 × 1 (i.e., a real number), D is a usual Euclidean distance matrix. Many interes...