Approximation by Interpolation: The Chebyshev Nodes

by Prof. Mama Foupouagnigni (AIMS / University of Yaounde 1, Cameroon)

Monday Dec 8, 2025, 4:15 PM → 5:15 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

Abstract: In this talk, we first revisit the well-known result stating that the Hermite interpolation polynomials of a function f continuous on $[-1, 1]$, with the zeros of the Chebyshev polynomials of the first kind as nodes, converge uniformly to $f$ on $[-1,1]$. Then we extend this result to obtain the uniform convergence of the Hermite interpolation polynomials, with the nodes taken as the zeros of the Chebyshev polynomials of the second, third and fourth kind, not on the interval $[-1,1]$ but rather on the intervals $[-\frac{2\sqrt{2}}{3}, \frac{2\sqrt{2}}{3}]$, $[-\frac{\sqrt{3}}{2}, 1]$ and $[-1, \frac{\sqrt{3}}{2}]$, respectively.

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 A short presentation of AIMS will follow the research talk:

The African Institute for Mathematical Sciences' efforts towards the Training of the next Generation of African Leading Scientists 

Abstract: In this talk, we first present the African Institute for Mathematical Sciences which is the first Pan-African Network of Centre of Excellence doing in the domain of Mathematical Sciences, Research and Public Engagement, located in 5 African countries: South Africa, Ghana, Senegal, Cameroon and Rwanda. Then, we present its achievements in 20 years, a great contribution to the training of the next generation of African leading scientists. Finally, we provide information about the AIMS Centre in Cameroon (www.aims-cameroon.org) and the areas of cooperation with German universities and the University of Bonn.