Best rational function approximation to Laplace transform inversion using a window function (*)

The best ra t ional f unc t i on a p p r o x i m a t i o n for Laplace t ransform inversion due to L o n g m a n is mod i f i ed by the i n t r o d u c t i o n o f an appropr ia te " w i n d o w " func t ion . This w i n d o w f u n c t i o n enables one to a p p r o x i m a t e the inverse t r ans fo rm f( t) by a linear c o m b i n a t i o n gn (t) o f n exponent ia l func t ions accura te ly in a given interval about a given po in t along the t -axis . It is p roved that the sequence o f a p p r o x i m a n t s {gn( t )}n =1 converges to f( t) in the mean . The m e t h o d is i l lustrated by some numer ica l examples .