Comparison of sequence accelerators for the Gaver method of numerical Laplace transform inversion

摘要

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 f(n)(t) - f(n-1)(t) similar to An(-2) as n --> infinity 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. (C) 2004 Elsevier Ltd. All rights reserved.