Comparison of sequence accelerators forthe Gaver method of numerical Laplace transform inversion

By P. Valko, Joseph Abate. 2004

249 citations recorded by the source corpus.

The sequence of Gaver functionals is useful in the numerical inversion of Laplace transforms. The convergence behavior of the sequence is logarithmic, therefore, an acceleration scheme is required. The accepted procedure utilizes Salzer summation, because in many cases the Gaver functionals have the asymptotic behavior @?"n(t) - @?"n(t) ~ An^-^2 as n -> ~ for fixed t. It seems that no other acceleration schemes have been investigated in this area. Surely, the popular nonlinear methods should be more effective. However, to our surprise, only one nonlinear method was superior to Salzer summation, namely the Wynn rho algorithm.

Subfields: Computational Mechanics, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/343b43934af8304560aedc4776cd024df582fa2f

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In Computational Mechanics

In Mathematical Physics

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Citations in the corpus

Some integral functionals of reflected SDEs and their applications in finance (2011, methodology): “This algorithm evaluates the inverse Laplace transform by calculating a series of the Gaver functional, and the series may be accelerated using the Wynn–Rho convergence acceleration scheme (Valkó and Abate 2004).”
A Unified Framework for Numerically Inverting Laplace Transforms (2006, methodology): “…the Gaver-Stehfest algorithm, e.g., see Gaver (1966), Stehfest (1970), Section 8 of Abate and Whitt (1992), Section 19.2 of Davies (2002), and Valko and Abate (2004); and Talbot’s method, e.g., see Talbot (1979), Murli and Rizzardi (1990), Evans (1993), Evans and Chung (2000), Section 19.8…”
Numerical Inversion of the Laplace Transform (2005, methodology): “Another type of algorithms is based on the Laguerre function expansion of the original f ¦ t § (cf. Weeks [12], Lyness and Giunta [13], Abate, Choudhury, Whitt [14] and Weideman [15]), i.e., f ¦ t § © ¨ e σt ∞ ∑ nC 0 a n e! bt L n ¦ 2bt § 5 " t # 0" (2.1) where L n ¦ t § denotes the Laguerre polynom”
On the conditional default probability in a regulated market: a structural approach (2011, methodology): “Instead, there are algorithms available for the numerical inversion of Laplace transforms (see Valkó and Vajda 2002, Valkó and Abate 2004 and section 4). and W( ; u, v) is given by ð ; u, vÞ ¼ Eð1Þ ðuÞE ð1Þ 1ðvÞ þ 2E ð0Þ ðuÞE ð0Þ 1ðvÞ, with E ð0Þ ðuÞ :¼ ffiffiffi 2 p e z 2=4 1F1 1 2 ; 1 2 ; 1 2…”