The CME method: Efficient numerical inverse Laplace transformation with Concentrated Matrix Exponential distribution

Numerical inverse Laplace transformation (NILT) is an important tool in the field of system modelling and performance analysis. The recently introduced CME method has many important advantages over the alternative numerical inverse Laplace transformation (NILT) methods. It avoids Gibbs oscillation (i.e., does not generate overshoot and undershoot), preserves the monotonicity of functions, its accuracy is gradually improving with the order, and it is numerically more stable than the alternative methods. In this paper we demonstrate these advantages and introduce our tool which implements the CME method and other popular NILT methods.