I'm creating a GUI interface for my Python computing class that is supposed to showcase a few types of numerical integration. One of the ones I want to put in as an option is Gauss–Legendre quadrature.
Part of the project is making a visualization of the method. The Newton–Cotes methods are easy to visualize. As well as is Monte Carlo integration. I'm stuck as to how I can visualize Gauss–Legendre quadrature though.
I was thinking about using a Lagrange polynomial fit with nodes at the roots of the Legendre polynomials. Is that the best way to do it?
Any ideas?
I don't this is possible, because from among the initial methods of numerical integration, this method and the Euler method are technical. However, you can show the geometry of legendre polynomials, which is the turning point of the Gauss-Legendre Quadrature. I recently did a job on my graduation about this, I'll be happy to clarify any doubts.