{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/conquering-the-pre-computation-in-two","title":"Conquering the pre-computation in two-dimensional harmonic polynomial transforms","arxiv_id":"1711.07866","date":"2017-11-21","proceeding":null,"authors":["Richard Mikael Slevinsky"],"abstract":"We describe a skeletonization of the spherical harmonic connection problem that reduces the storage and pre-computation to superoptimal complexities at the cost of increasing the execution time by the modest multiplicative factor of $\\mathcal{O}(\\log n)$. One advantage of accelerating the spherical harmonic connection problem over accelerating synthesis and analysis is that neighbouring layers (in steps of two) may be expanded in eachother's bases. The proposed skeletonization maximizes this interconnectivity by overlaying a dyadic partitioning on the connection problem. We derive the symmetric-definite banded generalized eigenvalue problem required to accelerate spherical harmonic transforms. We also include a full analysis of the weighted normalized Jacobi connection problem with applications to fast harmonic polynomial transforms on the disk, triangle, rectangle, deltoid, wedge, and any other geometry with a bivariate analogue of Jacobi polynomials.","url_abs":"http://arxiv.org/abs/1711.07866v1","url_pdf":"http://arxiv.org/pdf/1711.07866v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"conquering-the-pre-computation-in-two","repo_url":"https://github.com/MikaelSlevinsky/FastTransforms.jl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"conquering-the-pre-computation-in-two","repo_url":"https://github.com/JuliaApproximation/FastTransforms.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"conquering-the-pre-computation-in-two","repo_url":"https://github.com/MikaelSlevinsky/FastTransforms","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"conquering-the-pre-computation-in-two","repo_url":"https://github.com/UnofficialJuliaMirror/FastTransforms.jl-057dd010-8810-581a-b7be-e3fc3b93f78c","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"conquering-the-pre-computation-in-two","repo_url":"https://github.com/UnofficialJuliaMirrorSnapshots/FastTransforms.jl-057dd010-8810-581a-b7be-e3fc3b93f78c","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}