Dashnic-Zusmanovich class of matrices has been introduced in [1] as a generalization of the well-known strictly diagonally dominant class. In the same paper it has been shown that this class can be characterized by the special form of its “scaling” into an SDD matrix. Due to this fact, we can improve some known results about, for example, determinant estimation or Perron root estimation in the ...

If is the computed solution to a tridiagonal system Ax b obtained by Gaussian elimination, what is the "best" bound available for the error x and how can it be computed efficiently? This question is answered using backward error analysis, perturbation theory, and properties of the LU factorization of A. For three practically important classes of tridiagonal matrix, those that are symmetric posi...

We investigate and compare stable parallel algorithms for solving diagonally dominant and general narrow-banded linear systems of equations. Narrow-banded means that the bandwidth is very small compared with the matrix order and is typically between 1 and 100. The solvers compared are the banded system solvers of ScaLAPACK [11] and those investigated by Arbenz and Hegland [3, 6]. For the diagon...

In this paper, we study the class of relatively D-stable matrices and provide sufficient conditions for relative D-stability. We generalize well-known Hadamard inequality, to upper bounds determinants additive matrices. For some classes matrices, estimate sector gap between matrix spectra imaginary axis. apply developed technique obtain e.g. diagonally stable, dominant with Q2-scalings.

The original Hopfield neural networks model is adapted so that the weights of the resulting network are time varying. In this paper, the Discrete Hopfield neural networks with weight function matrix DHNNWFM the weight changes with time, are considered, and the stability of DHNNWFM is analyzed. Combined with the Lyapunov function, we obtain some important results that if weight function matrix W...