{"paper":{"title":"Efficient sum-of-exponentials approximations for the heat kernel and their applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Leslie Greengard, Shaobo Wang, Shidong Jiang","submitted_at":"2013-08-18T18:22:18Z","abstract_excerpt":"In this paper, we show that efficient separated sum-of-exponentials approximations can be constructed for the heat kernel in any dimension. In one space dimension, the heat kernel admits an approximation involving a number of terms that is of the order $O(\\log(\\frac{T}{\\delta}) (\\log(\\frac{1}{\\epsilon})+\\log\\log(\\frac{T}{\\delta})))$ for any $x\\in\\bbR$ and $\\delta \\leq t \\leq T$, where $\\epsilon$ is the desired precision. In all higher dimensions, the corresponding heat kernel admits an approximation involving only $O(\\log^2(\\frac{T}{\\delta}))$ terms for fixed accuracy $\\epsilon$. These approxi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3883","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":""},"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"}