The objective of this work is to provide a methodology for approximating globally optimal Fekete point configurations. This problem is of obvious interest in numerical mathematics and scientific modeling. Following a brief discussion of the pertinent analytical background, Lipschitz global optimization (LGO) is applied to determine --i.e., to numerically approximate-- Fekete point configurations. Next to the 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.

Optimization and variational techniques (msc 65K10), Linear programming (msc 90C05), Sensitivity, stability, parametric optimization (msc 90C31), Initial value problems (msc 65L05)
Modelling, Analysis and Simulation [MAS]
Modelling, Analysis and Computation

Pintér, J.D, Stortelder, W.J.H, & de Swart, J.J.B. (1997). Computation of elliptic Fekete point sets. Modelling, Analysis and Simulation [MAS]. CWI.