{"paper":{"title":"Numerically Stable Cholesky-QR on GPU via Mixed-Precision Randomized Preconditioning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Chao Chen, Ilse C. F. Ipsen, James E. Garrison","submitted_at":"2026-06-16T19:04:53Z","abstract_excerpt":"Cholesky-QR is among the fastest algorithms for computing the thin QR factorization of tall-and-skinny matrices on GPUs, relying entirely on BLAS-3 operations. However, it is numerically unstable: forming the Gram matrix squares the condition number, causing breakdown when $\\kappa_2(\\boldsymbol{A}) \\gtrsim 10^8$. We present MRCQR (Mixed-Precision Randomized Cholesky-QR), a stable GPU algorithm that addresses this limitation. MRCQR uses a subsampled randomized trigonometric transform to construct a preconditioner $\\boldsymbol{R}_s$ that reduces $\\kappa_2(\\boldsymbol{A}\\boldsymbol{R}_s^{-1})$ to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18411","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.18411/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}