In this work we present an algorithm for computing real zeros of a polynomial called cubic clipping. We write a given polynomial $p$ in Bernstein basis. Then we aproximate $p$ with a cubic polynomial $q$ using degree reduction on $p$. Using Cardano formula, we then compute the roots of $q$ which enclose zeros of $p$ and shorthen the length of the starting interval. Now we iterate this process, until we find zeros within the given accuracy. Lengths of the intervals containing zeros of $p$ have a convergence rate 4 for single roots, 2 for double roots and superlinear 4/3 for cubic roots.
|
