Speaker
Description
We will discuss the analytical characterisation of the Laplace transform inversion problem turned into a finite-dimensional linear system. This is done via a Gauss-Laguerre quadrature rule and regularised by means of a Tikhonov prescription. This, in the light of solutions obtained by, e.g., M. Hansen, et al. & M. Saccardi et al. via the implementation of other methods/regulation prescriptions will help gain understanding of the underlying connection granted by the singular value decomposition of the equivalent statements of the inverse problem when applied to lattice correlators. We show that all solutions for our problem when applied to sums of exponentials will be a superposition of a certain regularization of the Dirac delta. This allows us to devise several spectral reconstruction strategies based on minimization of a particular lagrangian 'cost' function