No abstract

SUMMARYZhao recently presented two accurate and universal approaches to the numerical inversion of the Laplace transform. Both approaches are based on irregularly spaced intervals. Compared with the conventional approach by Durbin, the computational burden of Zhao's approaches is significantly heavier. In this report, the author proposed refinements by which the efficiency of Zhao's approaches can be improved significantly. This is achieved by subdividing the entire integrating range into several sub-bands, but the sampling interval in each sub-band is constant. In this way, the computation is accelerated by either applying Clenshaw's recurrence or the Chirp-Z transform. The efficiency of both accelerating approaches is verified numerically by three examples, which makes Zhao's two approaches practicable. In addition, the history of applying the fast Fourier transform to the Laplace transform is reviewed briefly.

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