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

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

In Fitzpatrick and Flynn (J. Symbolic Comput. 13 (1992) 133), a Gröbner basis technique for multivariable Padé approximation problems was developed under a rather restrictive hypothesis on the shape of the numerator and denominator in relation to the approximation conditions desired. In this article, we show that their hypotheses can be replaced by other less stringent conditions, and we show h...

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.

On Padé Approximation of Some Practical Functions

on padé approximation of some practical functions

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Gröbner Basis Approach to Some Combinatorial Problems

We consider several simple combinatorial problems and discuss different ways to express them using polynomial equations and try to describe the Gröbner basis of the corresponding ideals. The main instruments are complete symmetric polynomials that help to express different conditions in rather compact way.