The Weighted Averages Algorithm Revisited

The classic weighted averages (WA) algorithm for the evaluation of Sommerfeld-like integrals is reviewed and reappraised. As a result, a new version of the WA algorithm, called generalized WA, is introduced. The new version can be considered as a generalization of the well established Hölder and Cèsaro means, used to sum divergent series. Generalized WA exhibits a more compact formulation, devoid of iterative and recursive steps, and a wider range of applications. It is more robust, as it provides a unique formulation, valid for monotonic and oscillating functions. The implementation of the new version is easier and more economical in terms of basic operations. Preliminary numerical examples show that generalized WA also outperforms in terms of accuracy the classic WA algorithm, which is currently recognized as the most competitive algorithm to evaluate Sommerfeld integral tails.