}
@Article{Kahinall14,
- title = "Parallel implementation of the Durand-Kerner algorithm for polynomial root-finding on GPU",
+ title = "Parallel implementation of the {D}urand-{K}erner algorithm for polynomial root-finding on GPU",
journal = "IEEE. Conf. on advanced Networking, Distributed Systems and Applications",
volume = "",
number = "",
%%$$ \exp \bigl( \ln(p(z)_{k})-ln(\ln(p(z)_{k}^{'}))- \ln(1- \exp(\ln(p(z)_{k})-ln(\ln(p(z)_{k}^{'})+\ln\sum_{i\neq j}^{n}\frac{1}{z_{k}-z_{j}})$$
\begin{equation}
\label{Log_H2}
-EA.EL: z^{k+1}=z_{i}^{k}-\exp \left(\ln \left(
+EA.EL: z^{k+1}_{i}=z_{i}^{k}-\exp \left(\ln \left(
p(z_{i}^{k})\right)-\ln\left(p'(z^{k}_{i})\right)- \ln
\left(1-Q(z^{k}_{i})\right)\right),
\end{equation}
\begin{equation}
\label{Log_H1}
Q(z^{k}_{i})=\exp\left( \ln (p(z^{k}_{i}))-\ln(p'(z^{k}_{i}))+\ln \left(
-\sum_{k\neq j}^{n}\frac{1}{z^{k}_{i}-z^{k}_{j}}\right)\right).
+\sum_{i\neq j}^{n}\frac{1}{z^{k}_{i}-z^{k}_{j}}\right)\right)i=1,...,n,
\end{equation}
This solution is applied when the root except the circle unit, represented by the radius $R$ evaluated in C language as:
