{"paper":{"title":"Real root finding for rank defects in linear Hankel matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Didier Henrion (LAAS), LIP6), Mohab Safey El Din (Syst\\`emes Polynomiaux, Simone Naldi (LAAS)","submitted_at":"2015-02-09T13:12:40Z","abstract_excerpt":"Let $H\\_0, ..., H\\_n$ be $m \\times m$\nmatrices with entries in $\\QQ$ and Hankel structure, i.e. constant skew diagonals.\nWe consider the linear Hankel matrix $H(\\vecx)=H\\_0+\\X\\_1H\\_1+...+\\X\\_nH\\_n$ and the problem of computing      sample  points in  each connected component of the real algebraic set defined by the rank constraint ${\\sf rank}(H(\\vecx))\\leq r$, for a given integer $r \\leq m-1$. Computing sample points in real algebraic sets defined by rank defects in linear matrices is a general problem that finds      applications in many areas such as control theory, computational geometry, o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02473","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}