Abstract

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., $10^{-1000}$).

Keywords

  1. truncated Laplace transform
  2. SVD

MSC codes

  1. 33F05
  2. 33E30
  3. 41A10
  4. 41A30
  5. 41A58
  6. 42C10
  7. 44A10
  8. 45A05
  9. 47A75
  10. 65D20

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Published In

cover image SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Pages: 1214 - 1235
ISSN (online): 1095-7170

History

Submitted: 8 October 2014
Accepted: 13 February 2015
Published online: 12 May 2015

Keywords

  1. truncated Laplace transform
  2. SVD

MSC codes

  1. 33F05
  2. 33E30
  3. 41A10
  4. 41A30
  5. 41A58
  6. 42C10
  7. 44A10
  8. 45A05
  9. 47A75
  10. 65D20

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