  Among the numerical inverse Laplace transformation (NILT) methods, those that
belong to the Abate-Whitt framework (AWF) are considered to be the most
efficient ones currently. It is a characteristic feature of the AWF NILT
procedures that they are independent of the transform function and the time
point of interest.
  In this work we propose an NILT procedure that goes beyond this limitation
and optimize the accuracy of the NILT utilizing also the transform function and
the time point of interest.
