The quadratic hermite-padé approximation

Quadratic Hermite-Padé polynomials associated with the exponential function

Generalized Hermite-Padé approximation for Nikishin systems of three functions

Nikishin systems of three functions are considered. For such systems, the rate of convergence of simultaneous interpolating rational approximations with partially prescribed poles is studied. The solution is described in terms of the solution of a vector equilibrium problem in the presence of a vector external field.

Analysis of Magneto-hydrodynamics Jeffery-Hamel Flow with Nanoparticles by Hermite-Padé Approximation

The combined effects of nanoparticle and magnetic field on the nonlinear Jeffery-Hamel flow are analyzed in the present study. The basic governing equations are solved analytically to nonlinear ordinary differential equation using perturbation method together with a semi-numerical analytical technique called Hermite- Padé approximation. The obtained results are well agreed with that of the Adom...

Quadratic Hermite-Pad6 Approximation to the Exponential Function

Approximation to exp of the form f~m(z) := pro(z) e -2z + qm(7.) e -Z + rm(z) = O(z3C"+t)-l), where p,., qm, and r,, are polynomials of degree at most m and p,, has lead coefficient 1 is considered. Exact asymptotics and explicit formulas are obtained for the sequences {~gm}, {P,,}, {qm}, and {rm}. It is observed that the above sequences all satisfy the simple four-term recursion: 1 Tin+ 3 = ~ ...

How well does the Hermite-Padé approximation smooth the Gibbs phenomenon?

In order to reduce the Gibbs phenomenon exhibited by the partial Fourier sums of a periodic function f , defined on [−π, π], discontinuous at 0, Driscoll and Fornberg considered so-called singular Fourier-Padé approximants constructed from the Hermite-Padé approximants of the system of functions (1, g1(z), g2(z)), where g1(z) = log(1 − z) and g2(z) is analytic, such that Re (g2(e)) = f(t). Conv...