In this work we present some matrix operators named circulant operators and their action on square matrices. This study on square matrices provides new insights into the structure of the space of square matrices. Moreover it can be useful in various fields as in agents networking on Grid or large-scale distributed self-organizing grid systems. Keywords— Pascal matrices, Binomial Recursion, Circ...

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 given nonnegative integer α, a matrix An of size n is called α-Toeplitz if its entries obey the rule An = [ar−αs] n−1 r,s=0. Analogously, a matrix An again of size n is called α-circulant if An = [ a(r−αs) modn ]n−1 r,s=0 . Such kind of matrices arises in wavelet analysis, subdivision algorithms and more generally when dealing with multigrid/multilevel methods for structured matrices and ...

Recurrent Neural Networks (RNNs) are becoming increasingly important for time series-related applications which require efficient and real-time implementations. The recent pruning based work ESE (Han et al., 2017) suffers from degradation of performance/energy efficiency due to the irregular network structure after pruning. We propose block-circulant matrices for weight matrix representation in...

Recurrent Neural Networks (RNNs) are becoming increasingly important for time series-related applications which require efficient and real-time implementations. The recent pruning based work ESE (Han et al., 2017) suffers from degradation of performance/energy efficiency due to the irregular network structure after pruning. We propose block-circulant matrices for weight matrix representation in...

Abstract. This paper is a continuation of the work in [11] and [2] on the problem of estimating by a linear estimator, N unobservable input vectors, undergoing the same linear transformation, from noise-corrupted observable output vectors. Whereas in the aforementioned papers, only the matrix representing the linear transformation was assumed uncertain, here we are concerned with the case in wh...

We propose geometrical methods for constructing square 01-matrices with the same number n of units in every row and column, and such that any two rows of the matrix have at most one unit in the same position. In terms of Design Theory, such a matrix is an incidence matrix of a symmetric configuration. Also, it gives rise to an n-regular bipartite graphs without 4-cycles, which can be used for c...

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...

In this paper we obtain [60,30,12], [64,32,12], [68,34,12], [72,36,12] doubly even self-dual codes as tailbitting convolutional codes with the smallest constraint length K=9. In this construction one information bit is modulo two add to the one of the encoder outputs and this row will replace the first row in the double circulant matrix. The pure double circulant construction with K=10 is also ...

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...