On the Analytical and Numerical Properties of the Truncated Laplace Transform I

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 (SVD) 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 exp -1000).

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Document Details

Document Type
Technical Report
Publication Date
Sep 05, 2014
Accession Number
ADA623097

Entities

People

  • Roy R. Lederman
  • Vladimir Rokhlin, Jr.

Organizations

  • Yale University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Coefficients
  • Computations
  • Continuous Spectra
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Integrals
  • Legendre Functions
  • Mathematics
  • Numbers
  • Polynomials
  • Real Numbers
  • Sequences
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Linear Algebra
  • Systems Analysis and Design