Technical Report CS0800

In an earlier paper by the author a detailed convergence and stability analysis of a generalization of the Richardson extrapolation process was given under certain conditions. In the present work these conditions are modified and relaxed considerably, and results are obtained on convergence and stability under the new conditions. As the previous ones, these new results are asymptotic in nature, and contain the former. The conditions of the present paper are naturally satisfied, e.g., by the trapezoidal rule approximations of finite range integrals of functions having algebraic and logarithmic end point singularities.