Two parallel implementations of Ehrlich-Aberth algorithm for root-finding of polynomials on multiple GPUs with OpenMP and MPI

Kahina Ghidouche (1) , Abderrahmane Sider (1) , Lilia Ziane Khodja (2) , Raphael Couturier (2)

1 UB - Université Abderrahmane Mira [Université de Béjaïa] = University Abderrahmane Mira [University of Béjaïa]
2 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)

Finding the roots of polynomials is a very important part of solving real-life problems but the higher the degree of the polynomials is, the less easy it becomes. In this paper, we present two different parallel algorithms of the Ehrlich-Aberth method to find roots of sparse and fully defined polynomials of high degrees. Both algorithms are based on CUDA technology to be implemented on multi-GPU computing platforms but each use different parallel paradigms: OpenMP or MPI. The experiments show a quasi-linear speedup by using up-to 4 GPU devices compared to 1 GPU to find the roots of polynomials of degree up-to 1.4 million. Moreover, other experiments show it is possible to find the roots of polynomials of degree up-to 5 million.

Domaines: Cryptographie et sécurité [cs.CR]; Calcul parallèle, distribué et partagé [cs.DC]; Technologies Émergeantes [cs.ET]; Informatique ubiquitaire; Système multi-agents [cs.MA]; Modélisation et simulation; Génie logiciel [cs.SE]

Kahina Ghidouche, Abderrahmane Sider, Lilia Ziane Khodja, Raphael Couturier. Two parallel implementations of Ehrlich-Aberth algorithm for root-finding of polynomials on multiple GPUs with OpenMP and MPI. International Conference on Computational Science and Engineering, Aug 2016, Paris, France. ⟨hal-02472585⟩