15950

Solver for Systems of Linear Equations with Infinite Precision on a GPU Cluster

Jiri Khun
Department of Computer Systems, Faculty of Information Technologies, Czech Technical University in Prague, Prague, Czech Republic
20th International Student Conference on Electrical Engineering, 2016

@article{khun2016solver,

   title={Solver for Systems of Linear Equations with Infinite Precision on a GPU Cluster},

   author={Khun, Jir{i}},

   year={2016}

}

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In this paper, we would like to introduce an accelerated solver for systems of linear equations with an infinite precision designed for GPU clusters. The infinite precision means that the system can provide a precise solution without any rounding error. These errors usually come from limited precision of floating point values within their natural computer representation. In a simplified description, the system is using modular arithmetic for transforming an original SLE into dozens of integer SLEs that are solved in parallel via a GPU cluster. In the final step, partial results are used for a calculation of the final solution. The usage of GPUs plays a key role in terms of performance because the whole process is computationally very intensive but also well scalable. An overall performance of the solver directly depends on the cluster’s configuration but it can offer the performance far beyond a single computing node.
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