Short Task: How can I find a interpolational quadrature formula with 2 points which interpolates all polynomials of second degree exactly.
2026-03-25 07:48:59.1774424939
numerical integration - quadrature of second degree
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It is only possible in dimension 1, as in superior dimensions, polynomials have more degrees of freedom. For arbitrary degree, you may look for https://en.wikipedia.org/wiki/Gaussian_quadrature.
In the case of integrating a polynomial of degree 2 (or 3 or less) over $[-1,1]$, you should take the points $\pm\sqrt{1/3}$ with unitary weights.