The Durand-Kerner Method Methods of extracting roots from a complex values polynomial is a well known research subject, but it is still open.
Literature abounds in theory studies and more and more efficient methods.
However, only few implementations have been realised and exploited, in any case not in the proportion of matrix calculation. There is a lot of scientific areas wishing spread out these methods, e.g. calculate the proper values of a matrix. The Newton method is the oldest extracting roots method, but it is a sequential one and it is not possible to parallelise it. Currently, there is few simultaneous methods where the roots are calculated by successive approximations. Part of them uses an iterative function which tends a vector to the root solutions.