Volterra type integral equation method for the radial Schrödinger equation: Single channel case

Kang, Sheon-Young

doi:10.1016/j.camwa.2004.08.004

Cited by 1 publication

(3 citation statements)

References 13 publications

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“…When we need to make a transition from V(1,2) to V(2,1), although the parameter dimensions are the same, just one of the model coefficients is common, say h (1) 1 . The remaining candidate coefficient, say h (2) 1 , 1 , should be proposed and h (1) 2 will be set to 0. For the reverse move from V(2,1) to V(1,2), the mechanism will be the same; h (1) 2 will be proposed and h (2) 1 , 1 will be set to 0.…”

Section: Trans-structural Rjmcmcmentioning

confidence: 99%

“…The remaining candidate coefficient, say h (2) 1 , 1 , should be proposed and h (1) 2 will be set to 0. For the reverse move from V(2,1) to V(1,2), the mechanism will be the same; h (1) 2 will be proposed and h (2) 1 , 1 will be set to 0. Coefficient updating mechanism for the moves can be defined as:…”

Section: Trans-structural Rjmcmcmentioning

confidence: 99%

“…Firstly, they are flexible enough to represent various nonlinear systems since continuously differentiable transfer functions can be easily approximated by Volterra models with Taylor series expansion. Moreover, various nonlinear differential equations such as Lotka-Volterra, Schrödinger [2] , can be rewritten as a Volterra system. Secondly, their inverses are also Volterra type which provides considerable ease in the identification of these systems [3] .…”

Section: Introductionmentioning

confidence: 99%

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Bayesian Volterra system identification using reversible jump MCMC algorithm

2017

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Volterra systems have had significant success in modelling nonlinear systems in various real-world applications. However, it is generally assumed that the nonlinearity degree of the system is known beforehand. In this paper, we contribute to the literature on Volterra system identification (VSI) with a numerical Bayesian approach which identifies model coefficients and the nonlinearity degree concurrently. Although this numerical Bayesian method, namely reversible jump Markov chain Monte Carlo (RJMCMC) algorithm has been used with success in various model selection problems, our use is in a novel context in the sense that both memory size and nonlinearity degree are estimated. The aforementioned study ensures an anomalous approach to RJMCMC and provides a new understanding on its flexible use which enables trans-structural transitions between different classes of models in addition to transdimensional transitions for which it is classically used. We study the performance of the method on synthetically generated data including OFDM communications over a nonlinear channel.

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