I am looking for a very fast polynomial root finder, hopefully with a matlab code. I don't need very accurate results, 2-3 decimal places would be fine. Also the method should be able to optionally take as input an initial guess of the roots. If the initial guess is close, this should speed the process up.
What do I need this for? I'm working on images and the method I'm implementing requires the roots of a polynomial to be found, at every pixel in the image. Given typical images are from 512x512 and up, the method has to be fast at the expense of accuracy if need be.