On Tchebycheff polynomials

Combinatorics of generalized Tchebycheff polynomials

By considering a family of orthogonal polynomials generalizing the Tchebycheff polynomials of the second kind we refine the corresponding results of De Sainte-Catherine and Viennot on Tchebycheff polynomials of the second kind (Lecture Notes in Mathematics, vol. 1171, 1985, Springer-Verlag, 120). © 2003 Elsevier Science Ltd. All rights reserved.

On a class of weak Tchebycheff systems

In this paper we study the approximation power, the existence of a normalized B-basis and the structure of a degree-raising process for spaces of the form span < 1, x, . . . , x, u(x), v(x) >, requiring suitable assumptions on the functions u and v. The results about degree raising are detailed for special spaces of this form which have been recently introduced in the area of CAGD.

Multi Agent Collaborative Search based on Tchebycheff decomposition

This paper presents a novel formulation ofMulti Agent Collaborative Search, for multi-objective optimization, based on Tchebycheff decomposition. A population of agents combines heuristics that aim at exploring the search space both globally (social moves) and in a neighborhood of each agent (individualistic moves). In this novel formulation the selection process is based on a combination of Tc...

Tchebycheff Approximation in a Compact Metric Space

On Classifications of Random Polynomials

&nbsp;Let $ a_0&nbsp;(omega),&nbsp;a_1&nbsp;(omega),&nbsp;a_2&nbsp;(omega), dots,&nbsp;a_n&nbsp;(omega)$&nbsp;be a sequence of independent random variables defined on a fixed probability space $(Omega, Pr,&nbsp;A)$. There are many known results for the expected number of real zeros of a polynomial&nbsp;$ a_0&nbsp;(omega) psi_0(x)+&nbsp;a_1&nbsp;(omega)psi_1 (x)+,&nbsp;a_2&nbsp;(omega)psi_2 (x)+...