Gaussian Quadrature Ranges with Observed Sound Speed Profiles

Dictionary learning of sound speed profiles

To provide constraints on the inversion of ocean sound speed profiles (SSPs), SSPs are often modeled using empirical orthogonal functions (EOFs). However, this regularization, which uses the leading order EOFs with a minimum-energy constraint on the coefficients, often yields low resolution SSP estimates. In this paper, it is shown that dictionary learning, a form of unsupervised machine learni...

Ray Stability for Background Sound Speed Profiles with Transition

In this paper deep ocean sound propagation through random media is considered. The study is conducted within a ray theory framework, which facilitates the assessment of ray stability. Model ocean environments where there is a gradual transition between two ambient sound speed profiles, a single duct Munk profile and a double duct profile taken in the Eastern North Atlantic are examined. We buil...

Anti-Gaussian quadrature formulas

An anti-Gaussian quadrature formula is an (n+ 1)-point formula of degree 2n− 1 which integrates polynomials of degree up to 2n+ 1 with an error equal in magnitude but of opposite sign to that of the n-point Gaussian formula. Its intended application is to estimate the error incurred in Gaussian integration by halving the difference between the results obtained from the two formulas. We show tha...

The Gaussian Quadrature Method

Trigonometric and Gaussian Quadrature

Some relationships are established between trigonometric quadrature and various classical quadrature formulas. In particular Gauss-Legendre quadrature is shown to be a limiting case of trigonometric quadrature. In an earlier paper [1] it was noted that there exist trigonometric and exponential analogs of Gaussian quadrature formulas. We now extend those results to show several interesting featu...