the matrix functions appear in several applications in engineering and sciences. the computation of these functions almost involved complicated theory. thus, improving the concept theoretically seems unavoidable to obtain some new relations and algorithms for evaluating these functions. the aim of this paper is proposing some new reciprocal for the function of block anti diagonal matrices. more...

In this paper we propose two new quasi-boundary value methods for regularizing the ill-posed backward heat conduction problems. With a standard finite difference discretization in space and time, obtained all-at-once nonsymmetric sparse linear systems have desired block ? -circulant structure, which can be utilized to design an efficient parallel-in-time (PinT) direct solver that built upon exp...

A complex orthogonal design that provides full diversity and full transmission rate for a space–time block code is not possible for more than two antennas. We design rate one codes which are quasi-orthogonal and provide partial diversity. The decoder of the proposed codes works with pairs of transmitted symbols instead of single symbols. A number of QuasiOrthogonal Space-Time Block Codes (QOSTB...

Unit memory convolutional codes with generator matrices, which are composed of circulant suhmatrices, are introduced. This structure facilitates the analysis as well as an efficient search for good codes. Equivalences among such codes and consider some of the basic structural properties are discussed. In particular, catastrophic encoders and minimal encoders are characterized and dual codes tre...

For a fixed positive integer n, let Wn be the permutation matrix corresponding to the permutation ( 1 2 · · · n− 1 n 2 3 · · · n 1 ) . In this article, it is shown that a symmetric matrix with rational entries is circulant if, and only if, it lies in the subalgebra of Q[x]/〈x−1〉 generated by Wn+W −1 n . On the basis of this, the singularity of graphs on n-vertices is characterized algebraically...

The symmetric circulant structure of many plants, including paper machines and distribution networks, is used to simplify the controller design for both 142-and H~-control, and to obtain super-optimality in the H®-case. Airliner-This paper is concerned with control of plants composed of n similar interacting subsystems. Such plants are common in practice and include paper machines, distribution...

In this article, we analyze the circulant structure of generalized circulant matrices to reduce the search space for finding lightweight MDS matrices. We first show that the implementation of circulant matrices can be serialized and can achieve similar area requirement and clock cycle performance as a serial-based implementation. By proving many new properties and equivalence classes for circul...

in this paper we consider the group algebra $r(c_2times‎ ‎d_infty)$‎. ‎it is shown that $r(c_2times d_infty)$ can be‎ ‎represented by a $4times 4$ block circulant matrix‎. ‎it is also‎ ‎shown that $mathcal{u}(mathbb{z}_2(c_2times d_infty))$ is‎ ‎infinitely generated‎.