{"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/an-efficient-method-to-verify-the-inclusion","title":"An Efficient Method to Verify the Inclusion of Ellipsoids","arxiv_id":"2211.06237","date":"2022-11-11","proceeding":null,"authors":["Julien Calbert","Lucas N. Egidio","Raphaël M. Jungers"],"abstract":"We present a novel method for deciding whether a given n-dimensional ellipsoid contains another one (possibly with a different center). This method consists in constructing a particular concave function and deciding whether it has any value greater than -1 in a compact interval that is a subset of [0,1]. This can be done efficiently by a bisection algorithm method that is guaranteed to stop in a finite number of iterations. The initialization of the method requires O(n^3) floating-point operations and evaluating this function and its derivatives requires O(n). This can be also generalized to compute the smallest level set of a convex quadratic function containing a finite number of n-ellipsoids. In our benchmark with randomly generated ellipsoids, when compared with a classic method based on semidefinite programming, our algorithm performs 27 times faster for ellipsoids of dimension n=3 and 2294 times faster for dimension n=100. We illustrate the usefulness of this method with a problem in the control theory field.","url_abs":"https://arxiv.org/abs/2211.06237v1","url_pdf":"https://arxiv.org/pdf/2211.06237v1.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":"an-efficient-method-to-verify-the-inclusion","repo_url":"https://github.com/egidioln/ellipsoidinclusion.jl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}