On the Analytical and Numerical Properties of the Truncated Laplace Transform
YALE UNIV NEW HAVEN CT
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The Laplace transform is frequently encountered in mathematics, physics, engineering and other areas. 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. In this dissertation, we construct efficient algorithms for the evaluation of the singular value decomposition SVD of such operators. The approach of this dissertation is somewhat similar to that introduced by Slepian et al. for the construction of prolate spheroidal wavefunctions in their classical study of the truncated Fourier 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. 10exp -1000.
- Numerical Mathematics