  We construct approximate Fekete point sets for kernel-based interpolation by
maximising the determinant of a kernel Gram matrix obtained via truncation of
an orthonormal expansion of the kernel. Uniform error estimates are proved for
kernel interpolants at the resulting points. If the kernel is Gaussian we show
that the approximate Fekete points in one dimension are the solution to a
convex optimisation problem and that the interpolants converge with a
super-exponential rate. Numerical examples are provided for the Gaussian
kernel.
