This work is devoted to a systematic investigation of triangular matrix forms of the Pascal Triangle. To start, the twelve matrix forms (collectively referred to as G-matrices) are presented. To highlight one way in which the G-matrices relate to each other, a set of four operators named circulant operators is introduced. These operators provide a new insight into the structure of the space of ...

A generic matrix A ∈ Cn×n is shown to be the product of circulant and diagonal matrices with the number of factors being 2n−1 at most. The demonstration is constructive, relying on first factoring matrix subspaces equivalent to polynomials in a permutation matrix over diagonal matrices into linear factors. For the linear factors, the sum of two scaled permutations is factored into the product o...

fifty years ago warren and root have introduced the shape factor. this fundamental parameter for modeling of naturally fractured reservoirs has been discussed stormily ever since. different definitions for shape factor have been suggested which all of them are heuristically based. recently, heinemann and mittermeir mathematically derived - based on the dual-continuum theorem assuming pseudo-ste...

In this paper we propose a 3D image reconstruction algorithm for a 3D Compton camera being developed at the University of Michigan. We present a mathematical model of the transition matrix of the camera which exploits symmetries by using an adapted spatial sampling pattern in the object domain. For each projection angle, the sampling pattern is uniform over a set of equispaced nested hemisphere...

We consider circulant preconditioners for Hermitian Toeplitz systems from the view point of function theory. We show that some well-known circulant preconditioners can be derived from convoluting the generating function f of the Toeplitz matrix with famous kernels like the Dirichlet and the Fej er kernels. Several circulant precondition-ers are then constructed using this approach. Finally, we ...

Spectral properties of sign symmetric matrices are studied. A criterion for sign symmetry of shifted basic circulant permutation matrices is proven, and is then used to answer the question which complex numbers can serve as eigenvalues of sign symmetric 3 × 3 matrices. The results are applied in the discussion of the eigenvalues of QM -matrices. In particular, it is shown that for every positiv...

An r × r matrix A = [aij] over a field F is called circulant if aij = a0, ( j−i) mod r . An [n = 2r, k = r] linear code over F = GF(q) is called double-circulant if it is generated by a matrix of the form [I A], where A is an r × r circulant matrix. In this work we first employ the Fourier transform technique to analyze and construct several families of double-circulant codes. The minimum dista...

In this talk, we present an efficient method for a convex optimization problem involving a large non-symmetric and non-Toeplitz matrix. The proposed method is an instantiation of ADMM (Alternating Direction Method of Multipliers) applied in Krylov subspaces. Our method shows a significant advantage in computational time for convex optimization problems involving general matrices of large size. ...

This paper studies two stochastic bulk arrival and bulk service queueing Models (A) and (B) with k varying environments. The system has infinite storing capacity and the arrival and service sizes are finite valued random variables. Matrix partitioning method is used to study the models. In Model (A) the maximum of the arrival sizes in all environments is greater than the maximum of the service ...

Anti-circulant tensors have applications in exponential data fitting. They are special Hankel tensors. In this paper, we extend the definition of anti-circulant tensors to generalized anticirculant tensors by introducing a circulant index r such that the entries of the generating vector of a Hankel tensor are circulant with module r. In the special case when r=n, where n is the dimension of the...