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252
A unified framework for numerically inverting Laplace transforms
 INFORMS Journal on Computing
, 2006
"... We introduce and investigate a framework for constructing algorithms to numerically invert Laplace transforms. Given a Laplace transform ˆ f of a complexvalued function of a nonnegative realvariable, f, the function f is approximated by a finite linear combination of the transform values; i.e., w ..."
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Cited by 18 (1 self)
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We introduce and investigate a framework for constructing algorithms to numerically invert Laplace transforms. Given a Laplace transform ˆ f of a complexvalued function of a nonnegative realvariable, f, the function f is approximated by a finite linear combination of the transform values; i
The FourierSeries Method For Inverting Transforms Of Probability Distributions
, 1991
"... This paper reviews the Fourierseries method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions. Some variants of the Fourierseries method are remar ..."
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Cited by 211 (52 self)
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This paper reviews the Fourierseries method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions. Some variants of the Fourierseries method
Supplement to “Power Algorithms for Inverting Laplace Transforms”
"... This is a supplement to the main paper, presenting additional experimental results not included in the main paper due to lack of space. The overall study investigates ways to create algorithms to numerically invert Laplace transforms within a unified framework proposed by Abate and Whitt (2006). Tha ..."
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Cited by 1 (0 self)
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This is a supplement to the main paper, presenting additional experimental results not included in the main paper due to lack of space. The overall study investigates ways to create algorithms to numerically invert Laplace transforms within a unified framework proposed by Abate and Whitt (2006
On the Laguerre method for numerically inverting Laplace transforms
 INFORMS Journal on Computing
, 1996
"... The Laguerre method for numerically inverting Laplace transforms is an old established method based on the 1935 TricomiWidder theorem, which shows (under suitable regularity conditions) that the desired function can be represented as a weighted sum of Laguerre functions, where the weights are coeff ..."
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Cited by 42 (7 self)
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The Laguerre method for numerically inverting Laplace transforms is an old established method based on the 1935 TricomiWidder theorem, which shows (under suitable regularity conditions) that the desired function can be represented as a weighted sum of Laguerre functions, where the weights
A Markovmodulated characterization of packetized voice and data traffic and related statistical multiplexer performance
 IEEE J. ON SELECTED AREAS IN COMMUN
, 1986
"... We study the performance of a statistical multiplexer whose inputs consist of a superposition of packetized voice sources and data. The performance analysis predicts voice packet delay distributions, which usually have a stringent requirement, as well as data packet delay distributions. The superpos ..."
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Cited by 288 (4 self)
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moments of voice and data delay distributions and queue length distributions. We also obtain LaplaceStieltjes transforms of the voice and data packet delay distributions, which are numerically inverted to evaluate tails of delay distributions. It is shown how the matrix analytic methodology can
Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps
 Proceedings of the National Academy of Sciences
, 2005
"... of contexts of data analysis, such as spectral graph theory, manifold learning, nonlinear principal components and kernel methods. We augment these approaches by showing that the diffusion distance is a key intrinsic geometric quantity linking spectral theory of the Markov process, Laplace operators ..."
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Cited by 257 (45 self)
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operators, or kernels, to the corresponding geometry and density of the data. This opens the door to the application of methods from numerical analysis and signal processing to the analysis of functions and transformations of the data. Abstract. We provide a framework for structural multiscale geometric
InfiniteSeries Representations Of Laplace Transforms Of Probability Density Functions For Numerical Inversion
, 1998
"... In order to numerically invert Laplace transforms to calculate probability density functions (pdf's) and cumulative distribution functions (cdf's) in queueing and related models, we need to be able to calculate the Laplace transform values. In many cases the desired Laplace transform value ..."
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Cited by 7 (1 self)
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In order to numerically invert Laplace transforms to calculate probability density functions (pdf's) and cumulative distribution functions (cdf's) in queueing and related models, we need to be able to calculate the Laplace transform values. In many cases the desired Laplace transform
INFINITESERIES REPRESENTATIONS OF LAPLACE TRANSFORMS OF PROBABILITY DENSITY FUNCTIONS FOR NUMERICAL INVERSION
, 1999
"... In order to numerically invert Laplace transforms to calculate probability density functions (pdf’s) and cumulative distribution functions (cdf’s) in queueing and related models, we need to be able to calculate the Laplace transform values. In many cases the desired Laplace transform values (e.g., ..."
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In order to numerically invert Laplace transforms to calculate probability density functions (pdf’s) and cumulative distribution functions (cdf’s) in queueing and related models, we need to be able to calculate the Laplace transform values. In many cases the desired Laplace transform values (e
JACOBI POLYNOMIALS USED TO APPROXIMATELY INVERT THE LAPLACE
"... Given the Laplace transform F(s) of a function f(t),we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is to construct a new method to evaluate the coefficients in the finite series expansion of f(t) in terms ..."
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Given the Laplace transform F(s) of a function f(t),we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is to construct a new method to evaluate the coefficients in the finite series expansion of f(t) in terms
Laplace Transforms Of Probability Density Functions With Series Representations
 AT&T Labs
, 1998
"... In order to numerically invert Laplace transforms to calculate probability distributions in queueing and related models, we need to be able to calculate the Laplace transform values. In many cases the desired Laplace transform values (e.g., of a waitingtime distribution) can be computed when the La ..."
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Cited by 1 (1 self)
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In order to numerically invert Laplace transforms to calculate probability distributions in queueing and related models, we need to be able to calculate the Laplace transform values. In many cases the desired Laplace transform values (e.g., of a waitingtime distribution) can be computed when
Results 1  10
of
252