Math 753/853 Newton's method

Newton's method is an algorithm for finding solutions $x$ of a nonlinear equation $f(x) = 0$ , where $f$ is differentiable. In general $f$ and $x$ can be multidimensional ( $f: \mathbb{R}^n \rightarrow \mathbb{R}^n$ ), but for now we'll just consider the one-dimensional case.

Some excellent online resources for Newton's method

Netwon's method, Wikipedia. Really nice explanation, animation of iteration of method, history, error analysis, and overview of what can go wrong.
Newton's method, Wolfram Alpha. Terse, error analysis, nice plots of Julia sets.
Newton's Method, Paul's Online Math Notes. Nice wordy description of algorithm with illustrative graphs, with two examples.

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Math 753/853 Newton's method

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