Quadratures with Superpower Convergence

Abstract: It is suggested that changing the variables of integration in quadrature calculations greatly improves the accuracy of the rule of means. The law of convergence becomes a superpower for infinitely smooth integrand functions. Its rate is much faster than that of a power law and is close to exponential. Power law convergence is achieved with the maximum attainable order of accuracy for integrand functions of limited smoothness. © 2022, Allerton Press, Inc.