Numerical Stability in an Inverse Scattering Problem.

Abstract

The main result of this paper is a stability theorem for a certain class of difference algorithms designed to give approximate solutions of a model inverse scattering problem in one dimension. This stability result guarantees the convergence of the approximate solutions to the exact solution of the problem as the grid of the difference scheme is refined. The results of numerical experiments are presented based on one of these schemes, in which second-order convergence is observed. Furthermore the cost (that is, the dependence on N of the number of arithmetic operations required to compute the solution at N grid points) of the algorithms discussed below is essentially optimal.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1979
Accession Number
ADA077135

Entities

People

  • W. W. Symes

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Acoustic Waves
  • Boundary Value Problems
  • Computational Science
  • Computations
  • Differential Equations
  • Elastic Waves
  • Equations
  • Formulas (Mathematics)
  • Integral Equations
  • Integrals
  • Intrusion Detectors
  • Inverse Problems
  • Partial Differential Equations
  • Scattering
  • United States
  • Volterra Equations
  • Waves

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Electronics Engineering