New stopping criteria for iterative root finding

A set of simple stopping criteria is presented, which improve the efficiency of iterative root finding by terminating the iterations immediately when no further improvement of the roots is possible. The criteria use only the function evaluations already needed by the root finding procedure to which they are applied. The improved efficiency is achieved by formulating the stopping criteria in terms of fractional significant digits. Test results show that the new stopping criteria reduce the iteration work load by about one-third compared with the most efficient stopping criteria currently available. This is achieved without compromising the accuracy of the extracted roots.