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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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mathematics7
2013-04-03 17:02:24

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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