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The convergence of the secant method is superlinear The purpose of this document is to show the following theorem: Theorem 1.1 Let {xk} ∞ k be the sequence produced by the secant method. Assume the sequence converges to a root of f(x) = 0, i.e., xk → x∞, f(x∞) = 0. Moreover, assume the root x ∞ is regular: f ′(x∞) ̸ = 0. Denote the error in the kth step by Ek = xk − x∞. Under these assumptions, we have The theorem is implied by three lemmas

Year: 2011

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