A Survey of Shanks’ Extrapolation Methods and Their Applications

Brezinski, Claude; Redivo–Zaglia, Michela

doi:10.1134/s0965542521050067

Cited by 4 publications

(2 citation statements)

References 39 publications

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“…In the following numerical examples, we rely on the ϵ method for convergence acceleration. This method is known to extend the region of convergence and even works when the radius of convergence is 0 [30].…”

Section: Light-traffic Analysismentioning

confidence: 99%

“…Wynn's ϵ-algorithm is an efficient implementation of Shank's transformation, which is the best all-purpose acceleration method according to [29]. Under non-stringent assumptions on the sequences, the transformation converges faster to the limit of the original series in the region of convergence and converges to the analytic continuation of diverging sequences [30].…”

Section: Introductionmentioning

confidence: 99%

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Performance of a Synchronisation Station with Abandonment

Fiems

2024

Mathematics

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The paper presents a Markovian queueing model for assessing the performance of synchronisation between stations in a production system. The system at hand consists of K distinct buffers, each buffer storing an item that is needed for the next production stage. Departures are immediate when all items are present. Due to the presence of multiple buffers, there is no reasonably fast way to calculate the stationary distribution of the Markov chain. Therefore, we focused on the series expansion of the stationary distribution in terms of the arrival rate. We provide a fast algorithm for calculating these terms. Comparing our results with stochastic simulation, we show that the expansion approach converges to the simulated values for a wide range of arrival rates.

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Section: Light-traffic Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%