- #1

FranzS

- 54

- 12

- TL;DR Summary
- What is the specific polynomial associated with the Gaussian-Legendre quadrature?

The

For the integration of non-polynomial functions, the

My question is: given a

In that case, how do you find it?

Will that polynomial be the best approximation (with degree

Thanks for your attention.

**n****-point**Gaussian-Legendre quadrature gives an exact value for the numerical integration of polynomials with degree up to**2**.*n*-1For the integration of non-polynomial functions, the

**n****-point**Gaussian-Legendre quadrature gives a good approximation as long as the function is well approximated by a polynomial with degree**2**.*n*-1My question is: given a

__non__-polynomial function to be integrated, is its**n****-point**Gaussian-Legendre quadrature associated with a specific polynomial with degree**2**?*n*-1In that case, how do you find it?

Will that polynomial be the best approximation (with degree

**2**) of the original function between the limits of integration? In other words, will that polynomial be the hypothetical result of applying a multilinear ("polynomial") regression (*n*-1**2**degree) to "all" the points of the original function between the limits of integration?*n*-1Thanks for your attention.