ON THE ANALYTICAL AND NUMERICAL PROPERTIES OF THE TRUNCATED LAPLACE TRANSFORM. PART II

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 left singular functions and singular values of the Truncated Laplace Transform. Together with the previously introduced algorithms for the evaluation of the right singular functions, these algorithms provide the singular value decomposition of the Truncated Laplace Transform. 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).