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...

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...

Several representations of the generalized Drazin inverse of an anti-triangular block matrix in Banach algebra are given in terms of the generalized Banachiewicz--Schur form.  

A novel block diagonalisation (BD)-based Multiuser multiple input multiple output (MU-MIMO)-aided relaying scheme is proposed for downlink transmissions, which does not require any channel state information at the base station (BS) and decomposes a MU-MIMO-aided relaying system into several parallel single-user MIMO-assisted relaying schemes. Furthermore, based on the proposed algorithm the opt...

In this paper we consider the following robust twoblock problem that arises in est,imation and in fullinformation control: minimize the worst-case H” norm of a two-block transfer matrix whose elements contain H”-norm-bounded modeling errors. We show that, when the underlying systems are single-input/singleoutput, and if the modeling errors are “small enough”, then t,he robust, two-block problem...

in this paper, the numerical technique based on hybrid bernoulli and block-pulse functions has been developed to approximate the solution of system of linear volterra integral equations. system of volterra integral equations arose in many physical problems such as elastodynamic, quasi-static visco-elasticity and magneto-electro-elastic dynamic problems. these functions are formed by the hybridi...