![]() We now treat the Levin transformations in more detail. We mentioned in Section 6.3 that the Levin-Sidi d (1)-transformation reduces to the Levin u-transformation when the R l in Definition 6.2.2 are chosen to be R l = l + 1. In the remainder of this work, we use the notation of this definition with no changes, as we did in previous chapters. We recall that the sequences mentioned here are in either b (1)/LOG or b (1)/LIN or b (1)/FAC described in Definition 15.3.2. (Analysis of the diagonal sequences turns out to be very difficult, and the number of meaningful results concerning this has remained very small.) Close this message to accept cookies or find out how to manage your cookie settings. ![]() Skip to main content Accessibility help We use cookies to distinguish you from other users and to provide you with a better experience on our websites. ![]() We show how these transformations are derived, and we provide a thorough analysis of their convergence and stability with respect to columns in their corresponding tables, as we did for the iterated Δ 2-process, the iterated Lubkin transformation, and the Shanks transformation. Practical Extrapolation Methods - June 2003. In this and the next few chapters, we discuss some nonlinear sequence transformations that have proved to be effective on some or all types of logarithmic, linear, and factorial sequences ∈ b (1). ![]()
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