Convergence Rate of Codes for Numerical Quardrature Techniques for Classical Ray Tracing.

Abstract

The estimated residual error (or its bound) for numerical quadratures is usually expressed in terms of a derivative of some order of the integrand or some residual factor of the integrand after factoring out a countable number of zeroes and singularities that occur along the integration path. The order of the derivative is a function of the number of sample points for evaluating the integrand. Regrettably, the magnitudes of these higher order derivatives are difficult enough to estimate for even analytic sound velocity profiles. In practice, observed sound velocity profiles, which are usually given in tabular form and include measurement errors, exacerbate our inability to assess the magnitudes of these higher order derivatives. An estimate of the residual error expressed in terms of a first derivative would be far more practical for both analytic and observed sound velocity profiles. Keywords: Ray tracing; Stieltjes measure.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1986
Accession Number
ADA191892

Entities

People

  • Edward R. Floyd

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Analytic Functions
  • Assembly
  • Convergence
  • Gaussian Quadrature
  • International Organizations
  • Measurement
  • Monitoring
  • Numerical Quadrature
  • Ray Tracing
  • Residuals
  • Second World War

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Electromagnetic Wave Scattering and Antenna Radiation Engineering