Fast and backward stable computation of roots of polynomials, Part II: backward error analysis; companion matrix and companion pencil · HackerPapers discussionshttps://hackerpaper.kaipfister.de/p/1611.02435/Collected HN comments and submissions linking this paper.enMon, 02 Nov 2026 11:16:22 GMTFast and backward stable computation of roots of polynomials, Part II: backward error analysis; companion matrix and companion pencil — mentioned by CyLithhttps://news.ycombinator.com/item?id=44891018urn:hackerpapers:mention:1611.02435:44891018Wed, 13 Aug 2025 17:04:40 GMT<p>The library only solves up to cubic equations, and the comments have a link to the following page: https://momentsingraphics.de/CubicRoots.html For general polynomials, it matters a great deal in what basis it is represented. The typical monomial basis is usually not the best from a numerical standpoint. I am aware of some modern methods such as this: https://arxiv.org/pdf/1611.02435 For polynomials expressed in e.g. a Bernstein basis, there are often much faster and stable tailored methods working solving for the eigenvalues of a companion matrix of a different form.</p><p><a href="https://hackerpaper.kaipfister.de/p/1611.02435/">Paper and discussion history</a>. A mention is not an endorsement.</p>math.NA