Two parallel implementations of Ehrlich-Aberth algorithm for root-finding of polynomials on multiple GPUs with OpenMP and MPI - Archive ouverte HAL Access content directly
Conference Papers Year : 2016

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

Abstract

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.
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Dates and versions

hal-02472585 , version 1 (10-02-2020)

Identifiers

  • HAL Id : hal-02472585 , version 1

Cite

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⟩
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