Math 753/853 Newton's method
Newton's method is an algorithm for finding solutions of a nonlinear equation , where is differentiable. In general and can be multidimensional (), but for now we'll just consider the one-dimensional case.
Some excellent online resources for Newton's method
, Wikipedia. Really nice explanation, animation of iteration of method, history, error analysis, and overview of what can go wrong.
, Wolfram Alpha. Terse, error analysis, nice plots of Julia sets.
, Paul's Online Math Notes. Nice wordy description of algorithm with illustrative graphs, with two examples.