Quasi-orthogonal Hadamard matrices and Mersenne with two three values of the elements, used in digital data processing, are considered, as well basis error-correcting codes algorithms for transforming orthogonal images. Attention is paid to structures cyclic symmetries antisymmetries. The connection between symmetry antisymmetry on a orders equal prime numbers, products close primes, composite ...

In this paper, we consider the H∞ controller design problem for both continuous-time and discrete-time linear time-invariant (LTI) systems via low order dynamic output feedback controllers. The existence condition of desired H∞ controllers is expressed as a feasibility problem of a bilinear matrix inequality (BMI) with respect to a coefficient matrix defining the controller and a Lyapunov matri...

We propose a divide-and-conquer algorithm for computing arbitrary functions of upper triangular matrices, which requires approximately the same number of arithmetic operations as Parlett’s algorithm. However, the new algorithm has better performance on computers with two levels of memory due to its block structure and thus, less memory-cache traffic requirements. Like Parlett’s algorithm, the n...

The quasi-orthogonal space time block coding (QO-STBC) over orthogonal frequency division multiplexing (OFDM) is investigated. Traditionally, QO-STBC does not achieve full diversity since the detection matrix of QO-STBC scheme is not a diagonal matrix. In STBC, the decoding matrix is a diagonal matrix which enables linear decoding whereas the decoding matrix in traditional QO-STBC does not enab...

The mathematical and numerical least squares solution of a general linear system of equations is discussed. Perturbation and differentiability theorems for pseudoinverses are given. Computational procedures for calculating least squares solutions using orthonormal transformations, multiplying matrices by a matrix of orthonormal basis vectors for the null-space of a given matrix, sequential proc...

Matrices with low-rank off-diagonal blocks are a versatile tool to perform matrix compression and to speed up various matrix operations, such as the solution of linear systems. Often, the underlying block partitioning is described by a hierarchical partitioning of the row and column indices, thus giving rise to hierarchical low-rank structures. The goal of this chapter is to provide a brief int...

Moment inequality for quadratic forms of random vectors is of particular interest in covariance matrix testing and estimation problems. In this paper, we prove a Rosenthal-type inequality, which exhibits new features and certain improvement beyond the unstructured Rosenthal inequality of quadratic forms when dimension of the vectors increases without bound. Applications to test the block diagon...

Stochastic Galerkin finite element discretizations of partial differential equations with coefficients characterized by arbitrary distributions lead, in general, to fully block dense linear systems. We propose two novel strategies for constructing preconditioners for these systems to be used with Krylov subspace iterative solvers. In particular, we present a variation of the hierarchical Schur ...

We consider the numerical solution of 3D linear elasticity equations. The investigated problem is described by a coupled system of second order elliptic partial differential equations. This system is then discretized by conforming or nonconforming finite elements. After applying the Finite Element Method (FEM) based discretization, a system of linear algebraic equations has to be solved. In thi...

The mathematical and numerical least squares solution of a general linear system of equations is discussed. Perturbation and differentiability theorems for pseudoinverses are given. Computational procedures for calculating least squares solutions using orthonormal transformations, multiplying matrices by a matrix of orthonormal basis vectors for the null-space of a given matrix, sequential proc...