Hierarchical Recursive Precision for Accelerating Symmetric Linear Solves on MXUs
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913174575382528 |
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| author | Carrica, Vicki Alomairy, Rabab Ringoot, Evelyne Edelman, Alan |
| author_facet | Carrica, Vicki Alomairy, Rabab Ringoot, Evelyne Edelman, Alan |
| contents | Symmetric positive-definite system solvers based on Cholesky factorization are fundamental to many scientific applications, such as climate modeling. We present a portable, nested recursive mixed-precision solver designed for Matrix Processing Units (MXUs), including NVIDIA Tensor Cores (H200) and AMD Matrix Cores (MI300X), that assigns low-precision FP16 arithmetic to large off-diagonal blocks, while preserving high precision on diagonal blocks to ensure numerical stability. The solver is implemented in Julia, providing a high-level, hardware-agnostic interface. We demonstrate up to a 5.07x speedup relative to the diagonal-precision vendor baseline, with 100x better accuracy than pure half precision on H200, providing higher accuracy than low-precision at higher speed than high-precision. Positive performance trends are also observed on MI300X, demonstrating broad applicability across GPUs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08082 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hierarchical Recursive Precision for Accelerating Symmetric Linear Solves on MXUs Carrica, Vicki Alomairy, Rabab Ringoot, Evelyne Edelman, Alan Distributed, Parallel, and Cluster Computing Emerging Technologies Mathematical Software Performance Symmetric positive-definite system solvers based on Cholesky factorization are fundamental to many scientific applications, such as climate modeling. We present a portable, nested recursive mixed-precision solver designed for Matrix Processing Units (MXUs), including NVIDIA Tensor Cores (H200) and AMD Matrix Cores (MI300X), that assigns low-precision FP16 arithmetic to large off-diagonal blocks, while preserving high precision on diagonal blocks to ensure numerical stability. The solver is implemented in Julia, providing a high-level, hardware-agnostic interface. We demonstrate up to a 5.07x speedup relative to the diagonal-precision vendor baseline, with 100x better accuracy than pure half precision on H200, providing higher accuracy than low-precision at higher speed than high-precision. Positive performance trends are also observed on MI300X, demonstrating broad applicability across GPUs. |
| title | Hierarchical Recursive Precision for Accelerating Symmetric Linear Solves on MXUs |
| topic | Distributed, Parallel, and Cluster Computing Emerging Technologies Mathematical Software Performance |
| url | https://arxiv.org/abs/2601.08082 |