Computing the real roots of a polynomial by the exclusion algorithm (Q1208054)

Let \(P(x)\) be a polynomial and \(Z=\{r|\) \(P(r)=0\}\), \(Z\subset\mathbb{R}\), \(\varepsilon>0\) be a given real number. The aim of the paper is to compute a set \(F_ \varepsilon\) satisfying \(Z\subset F_ \varepsilon\subset Z\cup[-K\varepsilon,K\varepsilon]\), where \(K\) is a constant independent of \(\varepsilon\). The paper presents some algorithms to solve this problem which require \(O(|\log \varepsilon|)\) steps and each step requires \(O(\log| \log\varepsilon |)\) multiplications. Some numerical examples are compared with well known polynomial root finding algorithms.