Convergence Rate of Codes for Numerical Quardrature Techniques for Classical Ray Tracing.
NAVAL OCEAN SYSTEMS CENTER SAN DIEGO CA
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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.
- Numerical Mathematics