Euclid algorithm, orthogonal polynomials, and generalized Routh-Hurwitz algorithm

The Routh-Hurwitz array and realization of characteristic polynomials

A "simplest Possible" Property of the Generalized Routh-hurwitz Conditions*

Euclid ’ s Algorithm Andrzej

The main goal of the paper is to prove the correctness of the Euclid’s algorithm for SCM. We define the Euclid’s algorithm and describe the natural semantics of it. Eventually we prove that the Euclid’s algorithm computes the Euclid’s function. Let us observe that the Euclid’s function is defined as a function mapping finite partial states to finite partial states of SCM rather than pairs of in...

A New Algorithm for Computing Orthogonal Polynomials

The aim of this paper is to present an algorithm for computing orthogonal polynomials. The Fast Fourier Transform completes the connection given by Draux between the three-term recurrence relationship and the Euclidian algorithm. Applications to Hankel systems and numerical examples illustrate our purpose.

Generalized Rook Polynomials and Orthogonal Polynomials

We consider several generalizations of rook polynomials. In particular we develop analogs of the theory of rook polynomials that are related to general Laguerre and Charlier polynomials in the same way that ordinary rook polynomials are related to simple Laguerre polynomials.