We describe an approach to the circulant Hadamard conjecture based on Walsh-Fourier analysis. We show that the existence of a circulant Hadamard matrix of order n is equivalent to the existence of a non-trivial solution of a certain homogenous linear system of equations. Based on this system, a possible way of proving the conjecture is proposed.

In this note, we study the notion of structured pseudospectra. We prove that for Toeplitz, circulant and symmetric structures, the structured pseudospectrum equals the unstructured pseudospectrum. We show that this is false for Hermitian and skew-Hermitian structures. We generalize the result to pseudospectra of matrix polynomials. Indeed, we prove that the structured pseudospectrum equals the ...

A set of fast real transforms including the well known Hartley transform is fully investigated. Mixed radix splitting properties of Hartley-type transforms are examined in detail. The matrix algebras diagonalized by the Hartley-type matrices are expressed in terms of circulant and (−1)-circulant matrices. © 2002 Elsevier Science Inc. All rights reserved.

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...

Given an ensemble of N × N random matrices, a natural question to ask is whether or not the empirical spectral measures of typical matrices converge to a limiting spectral measure as N → ∞. While this has been proved for many thin patterned ensembles sitting inside all real symmetric matrices, frequently there is no nice closed form expression for the limiting measure. Further, current theorems...

We prove that there is no circulant Hermitian complex Hadamard matrix of order n > 4.

Quantitative cerebral blood flow (CBF) can be obtained from dynamic susceptibility contrast (DSC) MRI using for instance the truncated singular value decomposition (tSVD). Block-circulant SVD and reformulated SVD (rSVD) are modified SVD approaches. The purpose of this study is to compare the different approaches. The optimal truncation thresholds (PSVD) for tSVD and block-circulant SVD are dete...

A typical Iranian carbonate matrix block surrounded by an open fracture was modeled in order to understand the fracture-matrix interaction and realize how to model the interaction best. The modeling was carried out by using a fine-scaled Eclipse model in the single porosity mode (the fractures were explicitly modeled). The model was extended to a stack of 6 matrix blocks to understand block-to-...

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...

a typical iranian carbonate matrix block surrounded by an open fracture was modeled in order to understand the fracture-matrix interaction and realize how to model the interaction best. the modeling was carried out by using a fine-scaled eclipse model in the single porosity mode (the fractures were explicitly modeled). the model was extended to a stack of 6 matrix blocks to understand block-to-...