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#1 2013-04-02 18:02:24

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.

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