Minimum-energy measures for singular kernels

We develop algorithms for energy minimization kernels with singularities. This problem arises in different fields, most notably the construction of space-filling sequences points where singularity guarantees a strong repelling property between these points. Numerical are based on approximating singular by non-singular ones, subsequent discretization and solving discrete problems. For kernels, we approximate an underlying completely monotone (briefly, CM) function bounded CM controlled accuracy. Theoretical properties suggested approximation studied some numerical results shown.