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Can one do better than linear convergence? Duh!
Expand f(x) in a Taylor series:
- f(x + ) = f(x) + f '(x) + f "(x) 2/2 + ...
For << x, drop higher order terms, so:
- f(x + ) = 0 = - f(x) / f '(x)
is correction added to current guess of root: