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Convergence acceleration of logarithmically convergent series avoiding summation

โœ Scribed by H.H.H. Homeier

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
255 KB
Volume
12
Category
Article
ISSN
0893-9659

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โœฆ Synopsis

There are several convergence acceleration methods that are based on the evaluation of partial sums sn for relatively large n, and thus, normally require the evaluation of all terms aj with 0 < j < n. Here, we show that it is possible to avoid the computation of the partials sums of high order if it is possible to evaluate a few terms aj for relatively large j. The effectiveness of the approach is demonstrated for the 1/z expansion that is a particularly difficult example of logarithmic convergence. (~) 1999 Elsevier Science Ltd. All rights reserved.

๐Ÿ“œ SIMILAR VOLUMES

Convergence acceleration of logarithmic
Convergence acceleration of logarithmic fixed point sequences
โœ Paul Sablonniere ๐Ÿ“‚ Article ๐Ÿ“… 1987 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 255 KB

Let (x,) be some sequence generated by x,+ 1 = f(x,) where i>1 For x 0 > 0 small, it converges to zero logarithmically, i.e. lim, xn+l/x . = 1, thus we need algorithms for accelerating its convergence. Using asymptotic expansions in the analysis of the A 2 and 02-algorithms leads to modified iter