Two-Stage Least Squares Algorithms with QR Decomposition for Simultaneous Equations Models on Heterogeneous Multicore and Multi-GPU Systems

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This paper analyzes the use of a multicore+multiGPU system for solving Simultaneous Equations Models by the Two-Stage Least Squares method with QR decomposition. The combination of CPU and GPU allows us to reduce the execution time in the solution of large SEM. When working on a heterogeneous system it is necessary to design dynamic and hybrid algorithms to exploit the full potential of the machine but the heterogeneity makes it diffcult. To obtain optimum performance, problems should be suitable and programming must be performed carefully. Our contribution shows that we can efficiently exploit the resources of the machine even for dense linear algebra problems of double data type where GPUs do not offer good performance, as occurs in some highly optimized libraries that use the hybrid programming CPU with GPU, such as CULA or MAGMA, where the speedup achieved is far from the theoretical.