On the stability of the J transformation

The stability of a large class of nonlinear sequence transformations is analyzed. Considered are variants of the J transformation 17]. Suitable variants of this transformation belong to the most successful extrapolation algorithms that are known 20]. Similar to recent results of Sidi, it is proved that the _p {J} transformations, the Weniger S transformation, the Levin transformation and a special case of the generalized Richardson extrapolation process of Sidi are S-stable. An efficient algorithm for the calculation of stability indices is presented. A numerical example demonstrates the validity of the approach. This revised version was published online in June 2006 with corrections to the Cover Date.