Accelerated convergence of sequences of quadrature approximations

Abstract A study is made of the use of the ϵ-algorithm for the acceleration of sequences of quadrature approximations. It is shown to be an effective extrapolation technique when applied to the appropriate sequence of approximations to finite range single and multidimensional integrals and some single dimensional indefinite integrals. It is also shown to have a more general range of applicability than certain more familiar techniques because it can be applied without modification to those finite range integrals whose integrands have boundary singularities.