Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §3.7 Newton’s Method (and Chaos), #33 · Calculus · Applications of derivatives

To speed up Newton's method, find the step … from

This problem is about competitors of Newton.

To speed up Newton's method, find the step $Δ x$ from $f (x_{n}) + Δ x f^{'} (x_{n}) + \frac{1}{2} (Δ x)^{2} f^{''} (x_{n}) = 0$ . Test on $f (x) = x^{2} - 1$ from $x_{0} = 0$ and explain.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §3.7 Newton’s Method (and Chaos), #33

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