On the Analytical and Numerical Properties of the Truncated Laplace Transform

Abstract

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. 10(exp -1000)).

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Document Details

Document Type
Technical Report
Publication Date
May 01, 2014
Accession Number
ADA624070

Entities

People

  • Roy R. Lederman

Organizations

  • Yale University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Coefficients
  • Continuous Spectra
  • Decomposition
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Integrals
  • Laguerre Functions
  • Legendre Functions
  • Mathematics
  • Numbers
  • Polynomials
  • Sequences
  • Square Roots
  • Theorems

Readers

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