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arXiv · 2605.25863

Linac: linear algebra with CUDA over finite fields

Giuseppe De Laurentis·Jack Franklin
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Abstract

Solving linear systems of polynomial equations is a ubiquitous problem in both mathematics and physics. The standard approach, Gaussian elimination, scales cubically with system size and often constitutes a computational bottleneck. The algorithm's inherent parallelism makes it well-suited for modern computing architectures, namely graphics processing units (GPUs), which offer significantly higher throughput than CPUs. Additionally, the use of finite fields -- integers modulo a prime -- in place of floating-point arithmetic offers a scalable solution to the issue of numerical precision loss, which becomes increasingly problematic at large system sizes. With Linac, we present a high-performance, open-source, parallel implementation of Gaussian elimination over finite fields and floating-point arithmetic. This tool has been developed for applications to analytic reconstruction of scattering amplitudes in quantum field theory.

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Giuseppe De Laurentis, Jack Franklin. 2026-05-25. Linac: linear algebra with CUDA over finite fields. https://arxiv.org/abs/2605.25863

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