The IRA procedures and other methods in convergence acceleration

The main contribution is a new approach to the are of convergence acceleration based on retardment, improvement and acceleration. For strictly monotone sets of sequences it is shown how to construct an accelerator or an improver from a retarder. This approach allows the construction of pairs of synchronizers (a retarder and an improver) needed by the IRA (Improver Retarder Algorithm) and RIA (Retarder Improver Algorithm), new extrapolation methods developed in this work. Other new synchronization processes, named curvature--type and logarithmic transforms, are introduced. Aitken's #DELTA#"2 synchronizable sets of real logarithmic sequences are reviewed since they are input to the IRA processes. The numerical features of several iterated methods based on IRA are discussed as well. An application of the E--algorithm to certain boundary value problems with singularities is also presentedAvailable from Fundacao para a Ciencia e a Tecnologia, Servico de Informacao e Documentacao, Av. D. Carlos I, 126, 1200 Lisboa / FCT - Fundação para o Ciência e a TecnologiaSIGLEPTPortuga