Anew approach for creating stable quadrature rules with preassigned points is proposed. The idea is to approximate a known stable quadrature rule by a local interpolation at the preassigned points. The construction cost of the method does not grow as the number of the preassigned points increases. The accuracy of the rule depends only on the accuracy of the chosen stable rule and that of the in...

Abstract. Good lattice quadrature rules are known to have O(N) convergence for periodic integrands with sufficient smoothness. Here it is shown that applying the baker’s transformation to lattice rules gives O(N) convergence for nonperiodic integrands with sufficient smoothness. This approach is philosophically and practically different than making a periodizing transformation of the integrand,...