Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 Help Me ! » Error of Gaussian quadrature rule » 2013-04-02 18:02:24

mathematics7
Replies: 0

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.

#2 Help Me ! » Degree of Precision and quadrature formula » 2013-04-02 17:51:15

mathematics7
Replies: 1

Devise a quadrature formula for

b
a
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.

Board footer

Powered by FluxBB