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 — gibson:teaching:fall-2016:math753:newtonmethod [2016/10/06 09:25] (current)gibson created 2016/10/06 09:25 gibson created 2016/10/06 09:25 gibson created Line 1: Line 1: + ====== 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 + * [[https://​en.wikipedia.org/​wiki/​Newton%27s_method|Netwon'​s method]], Wikipedia. Really nice explanation,​ animation of iteration of method, history, error analysis, and overview of what can go wrong. + * [[http://​mathworld.wolfram.com/​NewtonsMethod.html|Newton'​s method]], Wolfram Alpha. Terse, error analysis, nice plots of Julia sets. + * [[http://​tutorial.math.lamar.edu/​Classes/​CalcI/​NewtonsMethod.aspx|Newton'​s Method]], Paul's Online Math Notes. Nice wordy description of algorithm with illustrative graphs, with two examples. ​