Abstract
In this paper we consider numerical integration of smooth functions lying in a particular reproducing kernel Hilbert space. We show that the worst-case error of numerical integration in this space converges at the optimal rate, up to some power of a log N factor. A similar result is shown for the mean square worst-case error, where the bound for the latter is always better than the bound for the square worst-case error. Finally, bounds for integration errors of functions lying in the reproducing kernel Hilbert space are given. The paper concludes by illustrating the theory with numerical results.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have