{"paper":{"title":"Alternative Tilings for the Fast Multipole Method on the Plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.NA","authors_text":"Ramani Duraiswami, Yuancheng Luo","submitted_at":"2012-04-13T20:49:34Z","abstract_excerpt":"The fast multipole method (FMM) performs fast approximate kernel summation to a specified tolerance $\\epsilon$ by using a hierarchical division of the domain, which groups source and receiver points into regions that satisfy local separation and the well-separated pair decomposition properties. While square tilings and quadtrees are commonly used in 2D, we investigate alternative tilings and associated spatial data structures: regular hexagons (septree) and triangles (triangle-quadtree). We show that both structures satisfy separation properties for the FMM and prove their theoretical error bo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3105","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"}