(University of Oxford)

(University of Durham)

(KU Leuven)

(UNISA)

(UWC)

(RWTH Aachen University)

(Università di Bologna)

- Jon Chapman (University of Oxford)
- Title TBC

- Patrick Dorey (University of Durham)
- Title TBC

- Daan Huybrechs (KU Leuven)
- The benefits and pitfalls of redundancy in the approximation of functions

- Kerstin Jordaan (UNISA)
- Properties of orthogonal polynomials characterized by structural relations
In this talk we consider orthogonal polynomials that are characterized either by a structural relation of type \begin{equation}\pi(x)SP_n(x)=\sum_{k=-r}^{s}a_{n,n+k}P_{n+k}(x), \label{1}\end{equation}where $\pi(x)$ is a polynomial and $S$ is a linear operator that maps a polynomial of precise degree $n$ to a polynomial of degree $n-1$ or by \begin{equation}\label{2}\Pi(x)TP_n(x)=\sum_{k=-p}^{q}a_{n,n+k}P_{n+k}(x),\end{equation}where $\Pi(x)$ is a polynomial and $T$ is a linear operator that maps a polynomial of precise degree $n$ to a polynomial of degree $n-2$. It is understood that $S$ annihilates constants while $T$ annihilates polynomials of degree $1$. When $S=\displaystyle{\tfrac{d}{dx}}$, the structure relation (1) characterizes semiclassical orthogonal polynomials. We discuss properties of certain classes of semiclassical orthogonal polynomials. We characterize Askey-Wilson polynomials and their special or limiting cases as the only monic orthogonal polynomial solutions of (2) when $T=\mathcal{D}_q^2$ where $\mathcal{D}_q$ is the Askey-Wilson divided difference operator and $\Pi(x)$ is a polynomial of degree at most $4$. We use the structure relation (2) to derive bounds for the extreme zeros of Askey-Wilson polynomials.

- Properties of orthogonal polynomials characterized by structural relations
- Kailash Patidar (UWC)
- Modelling and robust simulations of slow-fast dynamical systems

- Holger Rauhut (RWTH Aachen University)
- Compressive sensing and its use for the numerical solution of parametric PDEs

- Valeria Simoncini (Università di Bologna)
- On the numerical solution of large-scale linear matrix equations

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