The aim of this paper is to show that the recently developed high performance
divide and conquer
algorithm for finding trigonometric sums can be applied to improve the performance of the Talbot’s method for the numerical inversion of the Laplace Transform on modern computer architectures including shared memory parallel computers. We also show how to vectorize the first stage of the Talbot’s method, namely computing all coefficients of the trigonometric sums used by the method. Numerical tests show that the improved method gives the same accuracy as the standard algorithm and it allows to utilize parallel processors.