We describe the dynamical system generated by Newton’s root-finding method from the point of view of Thurston’s characterization theory of rational maps, leading to a complete classification of all postcritically finite Newton maps, and outline an extension to a classification of all Newton maps (postcritically finite or not). We also discuss Newton’s method from the point of view of root finding; it has successfully found all roots of polynomials of degrees greater than 10
9.Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/node/7800