Numerical inverse Laplace transformation using concentrated matrix exponential distributions

Horväth, Gábor; Horváth, Illés; Almousa, Salah Al-Deen; Telek, Miklós

doi:10.1016/j.peva.2019.102067

Cited by 67 publications

(78 citation statements)

References 24 publications

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“…The parameters of CME distributions with low SCV have been calculated for up to order 1000 [15] and can be accessed at [16]. The CME method has several advantages compared to other NILT methods [12]. It is more stable numerically, provides smooth, over-and under-shooting free approximation even for discontinuous functions and, contrary to other methods of the family, its precision gradually improves when increasing its order (N).…”

Section: Cme Methodsmentioning

confidence: 99%

“…6. When g( ) > 0, according to (12) the second sum has positive terms only, so there are no cancellations. On the other hand, the approximation preserves nonnegativity, which might be a relevant property in certain applications.…”

Section: Interpretation Using Approximate Dirac Functionmentioning

confidence: 99%

“…In this section, we propose an approach for NIZT based on concentrated matrix geometric distributions, which we thus call CMG method and is the application of the CME (concentrated matrix exponential) method [12] for discrete time. The CME method is a numerical inverse Laplace transformation (NILT) procedure that uses the Abate-Whitt framework [13].…”

Section: Concentrated Matrix Geometric Distribution-based Inverse Tramentioning

confidence: 99%

“…If f n (t) was the Dirac impulse function at point T, then the Laplace inversion would be perfect, but depending on the weights η k and nodes β k , the function f n (t) only approximates the Dirac impulse function with a given accuracy. There are multiple different types of f n (t) functions that can be used for the approximation [12].…”

Section: Abate-whitt Framework For Numerical Inverse Laplace Transformentioning

confidence: 99%

See 3 more Smart Citations

Numerical Inverse Transformation Methods for Z-Transform

Horváth¹,

Mészáros

Telek

2020

Mathematics

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Numerical inverse Z-transformation (NIZT) methods have been efficiently used in engineering practice for a long time. In this paper, we compare the abilities of the most widely used NIZT methods, and propose a new variant of a classic NIZT method based on contour integral approximation, which is efficient when the point of interest (at which the value of the function is needed) is smaller than the order of the NIZT method. We also introduce a vastly different NIZT method based on concentrated matrix geometric (CMG) distributions that tackles the limitations of many of the classic methods when the point of interest is larger than the order of the NIZT method.

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Section: Cme Methodsmentioning

confidence: 99%

Section: Interpretation Using Approximate Dirac Functionmentioning

confidence: 99%

Section: Concentrated Matrix Geometric Distribution-based Inverse Tramentioning

confidence: 99%

Section: Abate-whitt Framework For Numerical Inverse Laplace Transformentioning

confidence: 99%

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Numerical Inverse Transformation Methods for Z-Transform

Horváth¹,

Mészáros

Telek

2020

Mathematics

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“…We also evaluate (32) in order to plot the position density of the particle in real and Laplace space (figure 1), using an implementation of the inverse Laplace transform algorithm [37,38]. Previously, due to the computational difficulty of solving the FFPE using the classical formulation of the absorbing boundary condition as a truncated dynamical operator, the position density had hitherto only been obtained using numerical simulations of Lévy flights.…”

Section: 21mentioning

confidence: 99%

First passage leapovers of Lévy flights and the proper formulation of absorbing boundary conditions

Wardak

2020

J. Phys. A: Math. Theor.

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An important open problem in the theory of Lévy flights concerns the analytically tractable formulation of absorbing boundary conditions. Although numerical studies using the correctly defined nonlocal approach have yielded substantial insights regarding the statistics of first passage, the resultant modifications to the dynamical equations hinder the detailed analysis possible in the absence of these conditions. In this study it is demonstrated that using the first-hit distribution, related to the first passage leapover, as the absorbing sink preserves the tractability of the dynamical equations for a particle undergoing Lévy flight. In particular, knowledge of the first-hit distribution is sufficient to fully determine the first passage time and position density of the particle, without requiring integral truncation or numerical simulations. In addition, we report on the first-hit and leapover properties of first passages and arrivals for Lévy flights of arbitrary skew parameter, and extend these results to Lévy flights in a certain ubiquitous class of potentials satisfying an integral condition.

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