Math Is Fun Forum

mathematics7

Member

Registered: 2013-04-02

Posts: 2

Error of Gaussian quadrature rule

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.