Finding elliptic Fekete points sets: two numerical solution approaches

摘要

The objective of this work is to provide a methodology for approximating globally optimal Fekete point configurations. This problem is of interest in numerical mathematics and scientific modeling. Following a brief discussion of the analytical background, Lipschitz global optimization (LGO) is applied to determine – i.e., to numerically approximate – Fekete point configurations. Next to this optimization approach, an alternative strategy by formulating a set of differential-algebraic equations (DAEs) of index 2 will be considered. The steady states of the DAEs coincide with the optima of the function to be minimized. Illustrative numerical results – with configurations of up to 150 Fekete points – are presented, to show the viability of both approaches.