{"paper":{"title":"An Optimized Sparse Approximate Matrix Multiply for Matrices with Decay","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.MS"],"primary_cat":"cs.NA","authors_text":"Matt Challacombe, Nicolas Bock","submitted_at":"2012-03-08T05:33:01Z","abstract_excerpt":"We present an optimized single-precision implementation of the Sparse Approximate Matrix Multiply (\\SpAMM{}) [M. Challacombe and N. Bock, arXiv {\\bf 1011.3534} (2010)], a fast algorithm for matrix-matrix multiplication for matrices with decay that achieves an $\\mathcal{O} (n \\log n)$ computational complexity with respect to matrix dimension $n$. We find that the max norm of the error achieved with a \\SpAMM{} tolerance below $2 \\times 10^{-8}$ is lower than that of the single-precision {\\tt SGEMM} for dense quantum chemical matrices, while outperforming {\\tt SGEMM} with a cross-over already for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1692","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}