In this paper, we introduce two approaches to compute the matrix hyperbolic tangent. While one of them is based on its own definition and uses exponential, other focused expansion Taylor series. For second approximation, analyse different alternatives evaluate corresponding polynomials. This resulted in three stable accurate codes, which implemented MATLAB numerically computationally compared b...

1. Introduction. In this chapter, we give an overview on methods to compute functions of a (usually square) matrix A with particular emphasis on the matrix exponential and the matrix sign function. We will distinguish between methods which indeed compute the entire matrix function, i.e. they compute a matrix, and those which compute the action of the matrix function on a vector. The latter task...

We present an explicit method to evaluate the nonnegativity of order 3 Matrix exponential functions.

This paper address the exponential stability for a class of switched systems with mixed time delays. Based on linear matrix inequalities and Lyapunov-Krasovskii functional approach, a geometrically switching rule for the exponential stability of the system is designed. The approach allows to compute simultaneously the two bounds that characterize the exponential stability rate of the solution. ...

The fundamental solution of a Hamiltonian system whose Hamiltonian H is positive definite and locally integrable is an entire function of exponential type. Its exponential type can be computed as the integral over √ det H . We show that this formula remains true in the indefinite (Pontryagin space) situation, where the Hamiltonian is permitted to have finitely many inner singularities. As a con...

We reconsider the construction of exponential fields in the quantized Liouville theory. It is based on a free-field construction of a continuous family or chiral vertex operators. We derive the fusion and braid relations of the chiral vertex operators. This allows us to simplify the verification of locality and crossing symmetry of the exponential fields considerably. The calculation of the mat...

We implement a second-order exponential integrator for semidiscretized advectiondiffusion-reaction equations, obtained by coupling exponential-like Euler and Midpoint integrators, and computing the relevant matrix exponentials by polynomial interpolation at Leja points. Numerical tests on 2D models discretized in space by Finite Differences or Finite Elements, show that the Leja-Euler-Midpoint ...

We consider certain classes of “exponential functions” on time scales, which are defined via dynamic equations and generalize the ordinary exponential function. In this paper we are interested first in the asymptotic behavior of these functions (say compared with the ordinary exponential) and second, how to efficiently calculate matrix analogues of these functions. For the latter question we di...

In this paper, we consider the global exponential stability of the equilibrium point of Hopfield neural networks with delays and impulsive perturbation. Some new exponential stability criteria of the system are derived by using the Lyapunov functional method and the linear matrix inequality approach for estimating the upper bound of the derivative of Lyapunov functional. Finally, we illustrate ...