Abstract When exploring the literature, it can be observed that operator obtained when applying Newton-like root finding algorithms to quadratic polynomials z 2 − c has same form regardless of which algorithm been used. In this paper, we justify why expression is obtained. This done by studying symmetries operators after a family degree d p ( ) = . Moreover, provide an iterative procedure obtai...

We present a computationally-efficient and numerically-robust algorithm for finding real roots of polynomials. It begins with determining the intervals where given polynomial is monotonic. Then, it performs robust variant Newton iterations to find root within each interval, providing fast guaranteed convergence satisfying error bound, as permitted by numerical precision used. For cubic polynomi...