Prove that the error of the Gaussian quadrature rule is
(integral of f (x)dx from a to b dx) - (∑ ie sum from i=1 to n of ci f(xi) = ((f^(2n)(z))/(2n)!)(integral of (∏ ie sum of products from i =1 to n of (x - xi)^2) from a to b dx)
for some z element of (a, b). Hint: Consider some kind of interpolation of f .
It would be nice if you could provide a clear proof so I could understand the error of the Gaussian quadrature rule.
Devise a quadrature formula for
f (x)dx (ie integral of f(x)dx from a to b) based on Hermit interpolation of f on the nodes x0 = a and x1 = b. Determine its degree of precision.
I would appreciate a solution so I can see how to determine the degree of precision for a question similar to one of my homework questions.