  This paper presents new quadrature rules for functions in a reproducing
kernel Hilbert space using nodes drawn by a sampling algorithm known as
randomly pivoted Cholesky. The resulting computational procedure compares
favorably to previous kernel quadrature methods, which either achieve low
accuracy or require solving a computationally challenging sampling problem.
Theoretical and numerical results show that randomly pivoted Cholesky is fast
and achieves comparable quadrature error rates to more computationally
expensive quadrature schemes based on continuous volume sampling, thinning, and
recombination. Randomly pivoted Cholesky is easily adapted to complicated
geometries with arbitrary kernels, unlocking new potential for kernel
quadrature.
