I intended the comment about multiplicity to be an exception to the first line about quadratic convergence You are correct that this is less than clear  Your suggested phrasing is fine  DurandKerner is Newtons method simultaneously on a vector of root guesses with the derivative of the polynomial approximated by the derivative of what the polynomial would be if its roots were the current set of guesses  This permits a lot of redundant computation to be eliminated  and the algorithm parallelized  If fx is a th degree polynomial and pqrs are root approximations the approximated polynomial is xpxqxrxs and its derivative at p is pqprps so a DurandKerner iteration for p would be p  p  fxpqprps and iterations of identical form for q r and s follow immediately  You are correct this looks a lot like the example given in the Jacobys method article