‎In this paper‎, ‎some algebraic and geometrical properties of the rank$-k$ numerical hulls of normal matrices are investigated‎. ‎A characterization of normal matrices whose rank$-1$ numerical hulls are equal to their numerical range is given‎. ‎Moreover‎, ‎using the extreme points of the numerical range‎, ‎the higher rank numerical hulls of matrices of the form $A_1 oplus i A_2$‎, ‎where $A_1...

In this paper a new approach to the modelling of ATM-traffic is proposed. The traffic is measured and characterised by its first and second order statistic moments. A Markov Modulated Poisson Process (MMPP) is used to capture the information in these two stochastic moments. Instead of a general MMPP, a circulant MMPP is used to reduce the computational cost. A circulant MMPP (CMMPP) is an MMPP ...

The permanent of an n x n matrix A = (a;j) is the matrix function ( 1) per A = ∑ al1r(1)••• a .. ",( .. )".C~" where the summation is over all permutations in the symmetric group, S ... An n x n matrix A is a circulant if there are scalars ab ... ,a,. such that (2) A= ∑ a;pi-l where P is the n x n permutation matrix corresponding to the cycle (12• .. n) in s". In general the computation of the ...

A) , (L J regular QC-LDPC code of length N is defined by a parity-check matrix L L p I p I p I p I p I p I p I p I p I H     (1) where 1 1    J j , 1 1    L l and   l j p I , represents the p p  circulant permutation matrix obtained by cyclically right-shifting the p p  identity matrix   0 I by l j p , positions, with. / L N p  For a specific QC-LDPC code we define the correspo...

We design heuristic algorithms to construct Hadamard matrices with two circulant cores. This hard combinatorial problem can be formulated in terms of objective functions of several binary variables, so that heuristic methodologies can be used. Our algorithms are based on local and tabu search and they use information on the geometry of the objective function landscapes. In addition, we use the ...

As part of a survey of state-of-the-art kernel approximation algorithms, we present a new sampling algorithm for circulant matrix construction to perform fast kernel matrix inversion in kernel ridge regression, comparing theoretical and experimental performance of that of multilevel circulant kernel approximation, incomplete Cholesky decomposition, and random features, all recent advances in th...

We associate to any given circulant complex matrix C another one E(C) such that E(E(C)) = C∗ the transpose conjugate of C. All circulant Hadamard matrices of order 4 satisfy a condition C4 on their eigenvalues, namely, the absolute value of the sum of all eigenvalues is bounded above by 4. We prove by a “descent” that uses our operator E that the only circulant Hadamard matrices of order n > 4,...

Purpose: Design of a preconditioner for fast and efficient parallel imaging and compressed sensing reconstructions. Theory: Parallel imaging and compressed sensing reconstructions become time consuming when the problem size or the number of coils is large, due to the large linear system of equations that has to be solved in l1 and l2-norm based reconstruction algorithms. Such linear systems can...