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Gaussian Quadrature Question

  1. Dec 3, 2007 #1
    I'm trying to make a generalized quadrature method and I seem to be running into some bizarre errors. For n=2 my answer is twice what it should be and for n greater the innaccuracy increases (answer/n is close but worse than answer/2 with n=2). My general algorithm is:
    p = nth legendre polynomial
    [itex]g = x \rightarrow f\left(\frac{b-a}{2}x+\frac{b+a}{2}\right)[/itex] where f is the function to integrate
    xs = n roots of p
    ws = weights based on value of n (2 => +/-0.57735026918963)

    I've checked my generation of legendre functions and they're consistently correct. I also generated a list of roots and verified some against wikipedia's list. Have I stupidly mangled the actual gaussian quadrature algorithm?

    I'm writing this in haskell so my code is 1:1 with the pseduo-code above.

    Thanks ahead for the help.

    Sorry if this is in the wrong forum, it's not coursework, but it is academic.
    Last edited: Dec 3, 2007
  2. jcsd
  3. Dec 3, 2007 #2


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    Science Advisor
    Gold Member

    I suggest you try it with f(x)=1 and see what the weights are.
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