Suppose that x∗ is a zero of f of multiplicity greater than 1. Prove that Newton’s method can only converge linearly to x∗
Added by Erick T.
Step 1
Since x* is a zero of f with multiplicity m (m > 1), we can express f(x) = (x - x*)^m · g(x) where g(x) is a function that is continuous near x* and g(x*) ≠ 0. Show more…
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