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When ??? (SIDER) +This solution is applied when the root except the circle unit, represented by the radius $R$ evaluated as: + +$$R = \exp( \log(DBL\_MAX) / (2*n) )$$ where $DBL\_MAX$ stands for the maximum representable double value. \section{The implementation of simultaneous methods in a parallel computer} \label{secStateofArt} @@ -356,7 +358,7 @@ parallelism that can be suitably exploited by SIMD machines. Moreover, they have fast rate of convergence (quadratic for the Durand-Kerner and cubic for the Ehrlisch-Aberth). Various parallel algorithms reported for these methods can be found -in~\cite{Cosnard90, Freeman89,Freemanall90,,Jana99,Janall99}. +in~\cite{Cosnard90, Freeman89,Freemanall90,Jana99,Janall99}. Freeman and Bane~\cite{Freemanall90} presented two parallel algorithms on a local memory MIMD computer with the compute-to communication time ratio O(n). However, their algorithms require @@ -382,6 +384,8 @@ GPUs, which details are discussed in the sequel. \section {A CUDA parallel Ehrlisch-Aberth method} +In the following, we describe the parallel implementation of Ehrlisch-Aberth method on GPU +for solving high degree polynomials. First, the hardware and software of the GPUs are presented. Then, a CUDA parallel Ehrlisch-Aberth method are presented. \subsection{Background on the GPU architecture} A GPU is viewed as an accelerator for the data-parallel and -- 2.39.5