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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2605.25863 |
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| _version_ | 1866917531673952256 |
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| author | De Laurentis, Giuseppe Franklin, Jack |
| author_facet | De Laurentis, Giuseppe Franklin, Jack |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25863 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Linac: linear algebra with CUDA over finite fields De Laurentis, Giuseppe Franklin, Jack Computational Physics High Energy Physics - Phenomenology High Energy Physics - Theory 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. |
| title | Linac: linear algebra with CUDA over finite fields |
| topic | Computational Physics High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2605.25863 |