We show that solving the frequency assignment problem is equivalent to solving a minimization problem involving spectral norms of matrices, if the link gain matrix is symmetric. Often the spectral norm is ideal for minimization problems, but not so in this case. We reformulate the minimization using the one-, innnity-and Frobenius norm. This allows us to deal with non symmetric link gain matric...

We show that solving the frequency assignment problem is equivalent to solving a minimization problem involving spectral norms of matrices, if the link gain matrix is symmetric. Often the spectral norm is ideal for minimization problems, but not so in this case. We reformulate the minimization using the one-, innnity-and Frobenius norm. This allows us to deal with non symmetric link gain matric...

In this paper, we introduce the concept of interval pseudo-homegeneous uninorms. We extend the concept of pseudo-homogeneity of specific functions for interval pseudo-homogeneous functions. It is studied two cases of interval pseudo-homogeneous uninorms, that is, interval pseudo-homogeneous tnorms and interval pseudo-homogeneous t-conorms. It is proved a form of interval pseudo-homogeneous t-no...

Emmanuel Preissmann, Olivier Lévêque Swiss Federal Institute of Technology Lausanne, Switzerland Abstract In this paper, we study spectral properties of generalized weighted Hilbert matrices. In particular, we establish results on the spectral norm, determinant, as well as various relations between the eigenvalues and eigenvectors of such matrices. We also study the asymptotic behaviour of the ...

for a ∈ mn, the schur multiplier of a is defined as s a(x) =a ◦ x for all x ∈ mn and the spectral norm of s a can be stateas ∥s a∥ = supx,0 ∥a ∥x ◦x ∥ ∥. the other norm on s a can be definedas ∥s a∥ω = supx,0 ω(ω s( ax (x ) )) = supx,0 ωω (a (x ◦x ) ), where ω(a) standsfor the numerical radius of a. in this paper, we focus on therelation between the norm of schur multiplier of product of matric...

Here, we will provide a spectral norm bound for the error of the approximation constructed by the BasicMatrixMultiplication algorithm. Recall that, given as input a m × n matrix A and an n× p matrix B, this algorithm randomly samples c columns of A and the corresponding rows of B to construct a m× c matrix C and a c× p matrix R such that CR ≈ AB, in the sense that some matrix norm ||AB −CR|| is...