We review the direct and inverse Laplace transforms on non-uniform time scales. introduce full backward-compatible unilateral studied their properties. also present corresponding integrals some examples.

other fields. However, the spectral properties of the Laplace Transform tend to complicate its numerical treatment; therefore, the closely related “Truncated” Laplace Transforms are often used in applications. We have constructed efficient algorithms for the evaluation of the Singular Value Decomposition (SVD) of Truncated Laplace Transforms; in the current paper, we introduce algorithms for th...

In this paper an optimal deterministic identification problem is solved in which a new measure for the misfit between data and system is minimized. It is shown that the misfit can be expressed as the Hankel norm of a specific operator. Optimal autonomous models are obtained by factorizing an optimal Hankel norm approximant of the Laplace transformed data matrix. An upperbound on the misfit betw...

Vol. 1 (2013) pp. 37-46. ALGORITHMS FOR UNEQUALLY SPACED FAST LAPLACE TRANSFORMS FREDRIK ANDERSSON⇤ Abstract. We develop fast algorithms for unequally spaced discrete Laplace transforms with complex parameters, which are approximate up to prescribed choice of computational precision. The algorithms are based on modifications of algorithms for unequally spaced fast Fourier transforms using Gauss...

In this work, we propose to price Parisian options using Laplace transforms. Not only do we compute the Laplace transforms of all the different Parisian options, but we also explain how to invert them numerically. We prove the accuracy of the numerical inversion.

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 waiting-time distribution) can be computed when the Laplace transform values of component probability density functions (pdf's) (e.g., of a service-tim...