![]() ![]() 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. Create lists, bibliographies and reviews: or Search WorldCat. Search for Library Items Search for Lists Search for Contacts Search for a Library. (Analysis of the diagonal sequences turns out to be very difficult, and the number of meaningful results concerning this has remained very small.) Practical extrapolation methods : their theory and application. 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. 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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