Computation of functions in the algebra of triangular Toeplitz matrices and numerical inversion of the Laplace transform

Embedding in the group of fractional powers yields a numerical functional calculus in the algebra of triangular Toeplitz matrices with one generator. Within this calculus, methods are described for the numerical inversion of the Laplace transform, differing from currently known methods in its greater stability to round-off errors. Examples are given of numerical inversion for the case in which the source functions are either regular or can be represented as singular generalized functions.