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Lagrange Interpolation

  1. Jan 27, 2010 #1
    1. The problem statement, all variables and given/known data I need to find a "Lagrange basis" corresponding to the function space spanned by the basis (1, x^2).

    2. Relevant equations I have been told the Lagrange polynomial is of the form

    (x-x_1)...(x-x_(k-1))(x-x_(k+1))..(x-x_n) / (x_k-x_1)...(x_k-x_(k-1))(x_k-x_(k+1))..(x_k-x_n)

    3. The attempt at a solution Since a + bx^2 is symmetric about the y axis, I am guessing one of the basis elements should be of the form

    (x-x_0)(x+x_0) / (x_1-x_0)(x_1+x_0) = (x^2 - x_0^2) / (x_1-x_0)(x_1+x_0). This has no terms in x so it seems to make sense. Not sure what to do about the other basis element.
     
    Last edited: Jan 27, 2010
  2. jcsd
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