Generalizations of Richardson Extrapolation with Applications to Numerical Integration

The application of extrapolation (or convergence acceleration) methods to the solution of problems in numerical analysis has become very widespread in recent years. One important area in which extrapolation methods have proved to be remarkably efficient is that of numerical integration. Of the methods that have proved to be useful in this area, the Richardson extrapolation process and some of its generalizations have been the subject of intense research. It is the purpose of this paper to survey briefly the recent developments relating to the generalizations of the Richardson extrapolation process with special emphasis on their application to the numerical evaluation of finite and infinite range integrals. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.