GPU Solver for Systems of Linear Equations with Infinite Precision

Abstract

In this paper, we would like to introduce a GPU accelerated solver for systems of linear equations with an infinite precision. 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 GPU. In the final step, partial results are used for a calculation of the final solution. The usage of GPU plays a key role in terms of performance because the whole process is computationally very intensive. The GPU solver can provide about one magnitude higher performance than a multithreaded one.