Computing the Incomplete Gamma Function to Arbitrary Precision

Winitzki, Serge

doi:10.1007/3-540-44839-x_83

Cited by 17 publications

(15 citation statements)

References 11 publications

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“…(9) is used for z P > (using at most ( ) O P terms), 0 a > and . a z < Thus, the calculation of the incomplete Gamma function ( , ) a z Γ for 0 z > requires ( ) O P long multiplications uniformly in z [15] . Thus using Eqs.…”

Section: Solution Of Membrane Equationmentioning

confidence: 99%

Event-driven simulation of integrate-and-fire models with spike-frequency adaptation

Lin

Zhang

2009

J. Electron.(China)

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The evoked spike discharges of a neuron depend critically on the recent history of its electrical activity. A well-known example is the phenomenon of spike-frequency adaptation that is a commonly observed property of neurons. In this paper, using a leaky integrate-and-fire model that includes an adaptation current, we propose an event-driven strategy to simulate integrate-and-fire models with spike-frequency adaptation. Such approach is more precise than traditional clock-driven numerical integration approach because the timing of spikes is treated exactly. In experiments, using event-driven and clock-driven strategies we simulated the adaptation time course of single neuron and the random network with spike-timing dependent plasticity, the results indicate that (1) the temporal precision of spiking events impacts on neuronal dynamics of single as well as network in the different simulation strategies and (2) the simulation time scales linearly with the total number of spiking events in the event-driven simulation strategies.

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Section: Solution Of Membrane Equationmentioning

confidence: 99%

Event-driven simulation of integrate-and-fire models with spike-frequency adaptation

Lin

Zhang

2009

J. Electron.(China)

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“…There exist many studies in the literature on different proposed methods for the numerical calculation of the incomplete gamma function [22][23][24]. MATLAB® also provides some tools for the calculation of the inverse incomplete gamma (gammaincinv) function.…”

Section: A Brief Description Of the Vortex Search Algorithmmentioning

confidence: 99%

Modified Vortex Search Algorithm for Real Parameter Optimization

Doğan

2016

Computer Science &Amp; Information Technology ( CS &Amp; IT )

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“…The number of Gamma function evaluations required increases as M increases, ranging from nine for small M to as large as several thousand for large M . In contrast, the proposed approximations consist of error functions, which are known to have lower computational complexity than both confluent hypergeometric and Gamma functions [11]. The integer mn approximation requires only two error function evaluations, the large SN R approximation requires one error function evaluation and one Gamma function evaluation, while the large mn approximation requires four error function evaluations.…”

Section: B Computational Complexitymentioning

confidence: 99%

Fast and Accurate Approximations for the Analysis of Energy Detection in Nakagami-m Channels

Horgan

Murphy

2013

IEEE Commun. Lett.

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Original citationHorgan, D.; Murphy C. C. (2013) Abstract-Previous research has identified several exact methods for the evaluation of the probability of detection for energy detectors operating on Nakagami-m faded channels. However, these methods rely on discrete summations of complicated functions, and so can take a prohibitively long time to evaluate. In this paper, three approximations for the probability of detection in Nakagami-m faded channels, having distinct regions of applicability, are derived. All have closed forms, and enable the fast and accurate computation of key performance metrics.

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Computing the Incomplete Gamma Function to Arbitrary Precision

Cited by 17 publications

References 11 publications

Event-driven simulation of integrate-and-fire models with spike-frequency adaptation

Event-driven simulation of integrate-and-fire models with spike-frequency adaptation

Modified Vortex Search Algorithm for Real Parameter Optimization

Fast and Accurate Approximations for the Analysis of Energy Detection in Nakagami-m Channels

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