Polynomial approximation and cubature at approximate Fekete and Leja points of the cylinder

The paper deals with polynomial interpolation, least-square approximation and cubature of functions defined on the rectangular cylinder, $K=D\times [-1,1]$, with $D$ the unit disk. The nodes used for these processes are the {\it Approximate Fekete Points} (AFP) and the {\it Discrete Leja Points} (DLP) extracted from suitable {\it Weakly Admissible Meshes} (WAMs) of the cylinder. From the analysis of the growth of the Lebesgue constants, approximation and cubature errors, we show that the AFP and the DLP extracted from WAM are good points for polynomial approximation and numerical integration of functions defined on the cylinder.