For two-dimensional (2-D) digital filters implemented by a block recursive equation, explicit relations between their frequency characteristics and those of scalar filter are obtained. Specifically, these include the relation between the discrete-time Fourier transform (DTFT) of the block recursive equation and that of the scalar 2-D difference equation, and the relation between the block matri...

Block tridiagonal matrices arise in applied mathematics, physics, and signal processing. Many applications require knowledge of eigenvalues and eigenvectors of block tridiagonal matrices, which can be prohibitively expensive for large matrix sizes. In this paper, we address the problem of the eigendecomposition of block tridiagonal matrices by studying a connection between their eigenvalues and...

In various cases we need to transform a process model into a matrix representation for further analysis. In this paper, we introduce the notion of Order Matrix, which enables unique representation of blockstructured process models. We present algorithms for transforming a block-structured process model into a corresponding order matrix and vice verse. We then prove that such order matrix consti...

Bimrocks are complex geomaterials that are defined as mixtures of rocks composed of geotechnically significant blocks within a matrix of finer texture. Bimslopes are made from bimrocks and are usually seen in weathered and shallow environments. Some characteristics of blocks affecting the strength of bimrocks include VBP (Volumetric Block Proportion), orientation, and arrangement, which have im...

Maximum margin criterion (MMC) is a well-known method for feature extraction and dimensionality reduction. However, MMC is based on vector data and fails to exploit local characteristics of image data. In this paper, we propose a two-dimensional generalized framework based on a block-wise approach for MMC, to deal with matrix representation data, that is, images. The proposed method, namely, bl...

We study the inhomogeneous generalization of a 1-dimensional AKLT spin chain model. Spins at each lattice site could be different. Under certain conditions, the ground state of this AKLT model is unique and is described by the Valence-Bond-Solid (VBS) state. We calculate the density matrix of a contiguous block of bulk spins in this ground state. The density matrix is independent of spins outsi...

Generalized Bhaskar Rao n-ary are defined. This paper studies with elements from abelian groups of Generalized Bhaskar Rao nary called Bhaskar Rao Bhaskar Rao a v b matrix of ±1 and such that the inner product of any two rows 0 and the matrix obtained of X by its absolute value the incidence matrix of the construction of infinite families of Balanced Balanced are Some construction methods and n...

Abstract. In this paper we consider the solution of Hermitian positive definite block-Toeplitz systems with small size blocks. We propose and study block diagonal and Schur complement preconditioners for such block-Toeplitz matrices. We show that for some block-Toeplitz matrices, the spectra of the preconditioned matrices are uniformly bounded except for a fixed number of outliers and this fixe...

In this paper, we give a weakly stable algorithm to solve a block Toeplitz system of linear equations. If the \look-ahead" steps taken to compute the parameters of the inversion formula for the block Toeplitz matrix are small compared to the order n of the matrix, the algorithm requires O(n 2) oating point operations. The parameters of the inversion formula are interpreted and computed in a rec...