![]() For the following subsections, failure of the method to converge indicates that the assumptions made in the proof were not met. If the assumptions made in the proof of quadratic convergence are met, the method will converge. Newton's method is only guaranteed to converge if certain conditions are satisfied. ![]() Then the expansion of f( α) about x n is: Proof of quadratic convergence for Newton's iterative method Īccording to Taylor's theorem, any function f( x) which has a continuous second derivative can be represented by an expansion about a point that is close to a root of f( x).
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