Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §3.7 Newton’s Method (and Chaos), #28 · Calculus · Applications of derivatives

Turn Problem 27 upside down, …, to find the quadratic iteration (10)…

This problem is about $x^{2} + 1 = 0$ and chaos.

Turn Problem 27 upside down, $1/ y_{n + 1} = 4 (y_{n - 1}) / y_{n}^{2}$ , to find the quadratic iteration (10) for $z_{n} = 1/ y_{n} = 1/ (1 + x_{n}^{2})$ .

This exercise builds on another exercise in its source book, which isn't shown here.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §3.7 Newton’s Method (and Chaos), #28

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