A new algorithm is developed for computing arbitrary real powers Ap of a matrix A ∈ Cn×n. The algorithm starts with a Schur decomposition, takes k square roots of the triangular factor T , evaluates an [m/m] Padé approximant of (1 − x)p at I − T 1/2 , and squares the result k times. The parameters k and m are chosen to minimize the cost subject to achieving double precision accuracy in the eval...

We present analytic estimates for the energy levels of N electrons (N = 2−5) in a two-dimensional parabolic quantum dot. A magnetic field is applied perpendicularly to the confinement plane. The relevant scaled energy is shown to be a smooth function of the parameter β=(effective Rydberg/effective dot energy)1/6. Two-point Pade approximants are obtained from the series expansions of the energy ...

This paper proposed a new approach of controller design. By using model matching method we design a PID controller for higher order system. A higher order model is reduced by Pade approximation and mixed method, then design a controller for reduced order model. We take a comparatively study between close loop response of higher order system and reduced order system. The model order reduction an...

The superiority of the convergence behavior of effective rotational Hamiltonians expressed in terms of Pade approximants over more conventional power series Hamiltonians is well known. For diatomics it is suggested that the failure of the conventional expansions is due to singularities in the complex Jplane. This theory is supported by numerical calculations on rotationally excited Ha with both...

A more interesting use of Padé approximation is “two-point Padé approximation” or Padé interpolation in which a Padé approximant for f(x) is constructed from two truncated Taylor series: one for when x is very small and one is for when x is very large. The Padé approximant in this method interpolates between the values at which f(x) is known. This method is directly applicable to perturbation t...

The mathematical structure imposed by the thermodynamic critical point motivates an approximant that synthesizes two theoretically sound equations of state: the parametric and the virial. The former is constructed to describe the critical region, incorporating all scaling laws; the latter is an expansion about zero density, developed from molecular considerations. The approximant is shown to yi...