Explanation of The Method
We use the three preceding iterates, xn−2, xn−1 and xn, with their function values, fn−2, fn−1 and fn. Applying the Lagrange interpolation formula to do quadratic interpolation on the inverse of f yields
We are looking for a root of f, so we substitute y = f(x) = 0 in the above equation and this results in the above recursion formula.
Read more about this topic: Inverse Quadratic Interpolation
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