{"paper":{"title":"Fast algorithms for spherical harmonic expansions, III","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.NA","authors_text":"Mark Tygert","submitted_at":"2009-10-28T17:03:05Z","abstract_excerpt":"We accelerate the computation of spherical harmonic transforms, using what is known as the butterfly scheme. This provides a convenient alternative to the approach taken in the second paper from this series on \"Fast algorithms for spherical harmonic expansions.\" The requisite precomputations become manageable when organized as a \"depth-first traversal\" of the program's control-flow graph, rather than as the perhaps more natural \"breadth-first traversal\" that processes one-by-one each level of the multilevel procedure. We illustrate the results via several numerical examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.5435","kind":"arxiv","version":6},"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"}