{"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/yet-another-eigenvalue-algorithm-for-solving","title":"Yet another eigenvalue algorithm for solving polynomial systems","arxiv_id":"2105.08472","date":"2021-05-18","proceeding":null,"authors":["Matías R. Bender","Simon Telen"],"abstract":"In latest years, several advancements have been made in symbolic-numerical eigenvalue techniques for solving polynomial systems. In this article, we add to this list. We design an algorithm which solves systems with isolated solutions reliably and efficiently. In overdetermined cases, it reduces the task to an eigenvalue problem in a simpler and considerably faster way than in previous methods, and it can outperform the homotopy continuation approach. We provide many examples and an implementation in the proof-of-concept Julia package EigenvalueSolver.jl.","url_abs":"https://arxiv.org/abs/2105.08472v2","url_pdf":"https://arxiv.org/pdf/2105.08472v2.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":"yet-another-eigenvalue-algorithm-for-solving","repo_url":"https://github.com/simontelen/JuliaEigenvalueSolver","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":"https://syntology.ai/paper/2105.08472","atlas_url":"https://app.syntology.ai/?focus=2105.08472","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}