Appendix B. Newton’s Method
To review Newton’s method very briefly, we are given a differentiable function f of a real variable x and we wish to solve the equation f(x) = 0 for x. Given a current estimate xn of a root of f, Newton’s method gives us a better estimate xn + 1, under suitable conditions, according to the formula
Here, f′(xn) is the derivative of f at x = xn. The derivation of this formula can be read off the figure below (solve for xn + 1).
The method works very well for simple, well-behaved functions such as polynomials, provided ...
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