Abstract
The high performance computing community has traditionally focused uniquely on the reduction of execution time, though in the last years, the optimization of energy consumption has become a main issue. A reduction of energy usage without a degradation of performance requires the adoption of energy-efficient hardware platforms accompanied by the development of energy-aware algorithms and computational kernels. The solution of linear systems is a key operation for many scientific and engineering problems. Its relevance has motivated an important amount of work, and consequently, it is possible to find high performance solvers for a wide variety of hardware platforms. In this work, we aim to develop a high performance and energy-efficient linear system solver. In particular, we develop two solvers for a low-power CPU-GPU platform, the NVIDIA Jetson TK1. These solvers implement the Gauss-Huard algorithm yielding an efficient usage of the target hardware as well as an efficient memory access. The experimental evaluation shows that the novel proposal reports important savings in both time and energy-consumption when compared with the state-of-the-art solvers of the platform.
Highlights
The solution of a system of linear equations of the form Ax = b, (1)where A ∈ Rn×n is a dense matrix, and b, x ∈ Rn×m represent respectively, the right-hand side vector of independent terms (RHS) and the sought-after solution, is the main computational problem in the solution of many scientific and engineering applications [1]
Huard presented the Gauss-Huard algorithm (GH) [6], which can be considered as an extension of the Gauss-Jordan elimination (GJE) algorithm for the solution of linear systems, and represents an alternative and reliable method when complemented with column pivoting [7]
Energy consumption has become a major issue in high performance computing, too
Summary
Where A ∈ Rn×n is a dense matrix, and b, x ∈ Rn×m represent respectively, the right-hand side vector of independent terms (RHS) and the sought-after solution, is the main computational problem in the solution. The main interest in this algorithm lies in its high degree of parallelism and its reduced number of memory operations This method usually delivers remarkable efficiency in modern hardware architectures that present a large number of computational units [4, 5]. Huard presented the Gauss-Huard algorithm (GH) [6], which can be considered as an extension of the GJE algorithm for the solution of linear systems, and represents an alternative and reliable method when complemented with column pivoting [7] This method presents the same computational cost as the LU-based solver, i.e., 2n3/3 flops. GPUs and the Intel Xeon Phi processors are successful exponents of this trend These new hardware platforms offer from tens to thousands of computational units, and are more energy-efficient than traditional multi-core processors.
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