Some remarks on Fitzpatrick and Flynn's Gröbner basis technique for Padé approximation

Gröbner bases and generalized Padé approximation

It is shown how to find general multivariate Padé approximation using the Gröbner basis technique. This method is more flexible than previous approaches, and several examples are given to illustrate this advantage. When the number of variables is small compared to the degree of approximation, the Gröbner basis technique is more efficient than the linear algebra methods in the literature.

Gröbner Bases, Padé Approximation, and Decoding of Linear Codes

This paper shows how Gröbner basis techniques can be used in coding theory, especially in the construction and decoding of linear codes. A simple algorithm is given for computing the reduced Gröbner basis of the vanishing ideal of a given set of finitely many points, and it is used for finding Padé approximation of any polynomial (given implicitly), which is a major step in decoding. A new meth...

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...

On Padé Approximation of Some Practical Functions

Some Remarks on Padé-approximations

Padé approximations are widely used to approximate a dead-time in continuous control systems. It provides a finite-dimensional rational approximation of a dead-time. However, the standard Padé approximation (recommended in many textbooks) with equal numeratorand denominator degree, exhibits a jump at time t=0. This is highly undesirable in simulating dead-times. To avoid this phenomena we shall...