On the use of Gauss quadrature in adaptive automatic integration schemes

The use of Kronrod's scheme for automatic adaptive integration is well known. In this paper we introduce Gauss integration rules combined with a new way of estimating the errors as basic rules in automatic adaptive integration schemes. On the basis of very limited numerical experiments it seems that our scheme may be as efficient and reliable as the Kronrod scheme.Supported by NAVF (The Norwegian Research Council for Arts and Sciences).