Regularization of a Fourier Series Method for the Laplace Transform inversion with real data

We propose a numerical method for computing a function, given its Laplace transform function on the real axis. The inversion algorithm is based on the Fourier series expansion of the unknown function and the Fourier coefficients are approximated using a Tikhonov regularization method. The key point of this approach is the use of the regularization scheme in order to improve the conditioning of the discrete problem: the value of the regularization parameter is that giving a tradeoff between the discretization error, including the regularization error, and the conditioning of the discrete problem.