Extensions of Drummond's process for convergence acceleration

• Autores: C. Brezinski, M. Redivo Zaglia
• Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 60, Nº. 12, 2010, págs. 1231-1241
• Idioma: inglés
• DOI: 10.1016/j.apnum.2010.04.015
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this paper, we give some new algebraic properties of a sequence transformation due to Drummond for accelerating the convergence. In the particular case where the terms of the sequence to be transformed are the partial sums of a formal power series, this transformation leads to Padé-type approximants. Then, using various operators, some extensions of Drummond's process are proposed, and their properties are given. A new expression for the E-transformation, using generalized divided differences, is obtained, and it is also generalized. The recurrence relation for these differences can be used for its implementation, and the Ford�Sidi algorithm is also related to them. Lubkin's T and W-transformations, which could be related to Drummond's, are discussed in Appendix A.