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Notes on Numerical Analysis I. Polynomial Iteration
Canadian mathematical bulletin, Tome 2 (1959) no. 2, pp. 97-110

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Let f(x) be a real analytic function of the real variable x and α a simple root of the equation f(x) = 0. It is well known that a function φ(x) can be associated with the equation in many different ways such that (i) α is a root of the equation φ(x), i.e. α is a fixed point (invariant point) of the function φ(x); (ii) 
Schwerdtfeger, Hans. Notes on Numerical Analysis I. Polynomial Iteration. Canadian mathematical bulletin, Tome 2 (1959) no. 2, pp. 97-110. doi: 10.4153/CMB-1959-015-4
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