{"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/compensated-de-casteljau-algorithm-in-k-times","title":"Compensated de Casteljau algorithm in $K$ times the working precision","arxiv_id":"1808.10387","date":"2018-08-30","proceeding":null,"authors":["Danny Hermes"],"abstract":"In computer aided geometric design a polynomial is usually represented in Bernstein form. This paper presents a family of compensated algorithms to accurately evaluate a polynomial in Bernstein form with floating point coefficients. The principle is to apply error-free transformations to improve the traditional de Casteljau algorithm. At each stage of computation, round-off error is passed on to first order errors, then to second order errors, and so on. After the computation has been \"filtered\" $(K - 1)$ times via this process, the resulting output is as accurate as the de Casteljau algorithm performed in $K$ times the working precision. Forward error analysis and numerical experiments illustrate the accuracy of this family of algorithms.","url_abs":"http://arxiv.org/abs/1808.10387v2","url_pdf":"http://arxiv.org/pdf/1808.10387v2.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":"compensated-de-casteljau-algorithm-in-k-times","repo_url":"https://github.com/dhermes/k-compensated-de-casteljau","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}