Multidimensional pseudo Leja sequences

The one-dimensional pseudo-Leja sequences, presented as an alternative to Leja sequences in [5], offer good interpolation nodes for approximating holomorphic functions. We propose a definition for multidimensional pseudo-Leja sequences related to a compact set K in the complex space 􏰁p, which extends the concept of the one-dimensional version and the multidimensional Leja sequences. We show that these sequences can be used to calculate the transfinite diameter of K, suggesting their potential suitability for multivariate polynomial interpolation. We also present a relation to the pluricomplex Green function associated to K. Subsequently, we demonstrate that intertwining pseudo Leja sequences results in another pseudo Leja sequence. Additionally, we provide a method for computing pseudo Leja sequences using discrete meshes.