{"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/adjusted-least-squares-fitting-of-algebraic","title":"Adjusted least squares fitting of algebraic hypersurfaces","arxiv_id":"1412.2291","date":"2014-12-06","proceeding":null,"authors":["Konstantin Usevich","Ivan Markovsky"],"abstract":"We consider the problem of fitting a set of points in Euclidean space by an\nalgebraic hypersurface. We assume that points on a true hypersurface, described\nby a polynomial equation, are corrupted by zero mean independent Gaussian\nnoise, and we estimate the coefficients of the true polynomial equation. The\nadjusted least squares estimator accounts for the bias present in the ordinary\nleast squares estimator. The adjusted least squares estimator is based on\nconstructing a quasi-Hankel matrix, which is a bias-corrected matrix of\nmoments. For the case of unknown noise variance, the estimator is defined as a\nsolution of a polynomial eigenvalue problem. In this paper, we present new\nresults on invariance properties of the adjusted least squares estimator and an\nimproved algorithm for computing the estimator for an arbitrary set of\nmonomials in the polynomial equation.","url_abs":"http://arxiv.org/abs/1412.2291v2","url_pdf":"http://arxiv.org/pdf/1412.2291v2.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":"abstracts"},"code_links":[{"paper_slug":"adjusted-least-squares-fitting-of-algebraic","repo_url":"https://github.com/slra/als-fit","is_official":1,"mentioned_in_paper":1,"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}