Gaussian Integration Techniques

Gaussian quadrature is a numerical technique that improves integration accuracy by evaluating functions at specific nodes based on orthogonal polynomials.

Chebyshev-Gauss quadrature uses Chebyshev polynomial roots to determine nodes, which reduces oscillations and errors near the boundaries.

This method can integrate functions over arbitrary intervals by transforming them to fit the Chebyshev-Gauss form.

Chebyshev-Gauss quadrature is efficiently implemented using vectorization techniques, which speeds up the integration process.