ON THE ANALYTICAL AND NUMERICAL PROPERTIES OF THE TRUNCATED LAPLACE TRANSFORM I

The Laplace Transform is frequently encountered in mathematics, physics, engineering, and other fields. However, the spectral properties of the Laplace Transform tend to complicate its numerical treatment; therefore, the closely related "Truncated" Laplace Transforms are often used in applications. We have constructed efficient algorithms for the evaluation of the Singular Value Decomposition of Truncated Laplace Transforms; in the current paper, we introduce algorithms for the evaluation of the right singular functions and singular values of Truncated Laplace Transforms. Algorithms for the computation of the left singular functions will be introduced separately in an upcoming paper. The resulting algorithms are applicable to all environments likely to be encountered in applications, including the evaluation of singular functions corresponding to extremely small singular values (e.g., 10–1000).