Mohamed Chaouki Tarchi

activity

20202025

collaborators

4 papers

math.NA2025

Numerical approach for solving problems arising from polynomial analysis

Yousra Gati, Vladimir Petrov Kostov, Mohamed Chaouki Tarchi

This paper deals with the use of numerical methods based on random root sampling techniques to solve some theoretical problems arising in the analysis of polynomials. These methods…

math.CA2023

Degree $6$ hyperbolic polynomials and orders of moduli

Yousra Gati, Vladimir Petrov Kostov, Mohamed Chaouki Tarchi

We consider real univariate degree $d$ real-rooted polynomials with non-vanishing coefficients. Descartes' rule of signs implies that such a polynomial has $c ~$ positive and…

math.CA2023

Further than Descartes' rule of signs

Yousra Gati, Vladimir Petrov Kostov, Mohamed Chaouki Tarchi

The {\em sign pattern} defined by the real polynomial $Q := Σ_{j = 0}^{d} a_{j} x^{j}$ , $a_{j} \neq = 0$ , is the string $σ (Q) := (sgn (a_{d}), \dots, sgn (a_{0}))$ . The quantities $…

math.CA2020

Sign patterns and rigid moduli orders

Yousra Gati, Vladimir Petrov Kostov, Mohamed Chaouki Tarchi

We consider the set of monic degree $d$ real univariate polynomials $Q_{d} = x^{d} + \sum_{j = 0}^{d - 1} a_{j} x^{j}$ and its {\em hyperbolicity domain} $Π_{d}$ , i.e. the subset of values of the coef…

Numerical approach for solving problems arising from polynomial analysis

Degree 6 hyperbolic polynomials and orders of moduli

Further than Descartes' rule of signs

Sign patterns and rigid moduli orders

Degree $6$ hyperbolic polynomials and orders of moduli