{"doi":"10.48550/arxiv.2406.05922","title":"Fast expansion into harmonics on the ball","abstract":"We devise fast and provably accurate algorithms to transform between an $N\\times N \\times N$ Cartesian voxel representation of a three-dimensional function and its expansion into the {ball harmonics}, that is, the eigenbasis of the Dirichlet Laplacian on the unit ball in $\\mathbb{R}^3$. Given $\\varepsilon > 0$, our algorithms achieve relative $\\ell^1$ - $\\ell^\\infty$ accuracy $\\varepsilon$ in time $O(N^3 (\\log N)^2 + N^3 |\\log \\varepsilon|^2)$, while the naïve direct application of the expansion operators has time complexity $O(N^6)$. We illustrate our methods on numerical examples.","journal":"arXiv (Cornell University)","year":2024,"id":498397,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":0,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9572,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2024-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":954147,"name":"Nicholas F. Marshall","orcid":"0000-0002-1871-6862","position":1,"is_corresponding":false},{"id":1095163,"name":"Oscar Mickelin","orcid":"0000-0003-0167-1992","position":2,"is_corresponding":false},{"id":285325,"name":"Amit Singer","orcid":"0000-0002-6975-7955","position":3,"is_corresponding":false},{"id":1318661,"name":"Joe Kileel","orcid":"0000-0001-9926-9170","position":0,"is_corresponding":true}],"reference_count":0,"raw_metadata":null,"created_at":"2026-07-19T02:09:42.181447Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}