{"paper":{"title":"Fast and accurate con-eigenvalue algorithm for optimal rational approximations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"G. Beylkin, T. S. Haut","submitted_at":"2010-12-15T00:10:54Z","abstract_excerpt":"The need to compute small con-eigenvalues and the associated con-eigenvectors of positive-definite Cauchy matrices naturally arises when constructing rational approximations with a (near) optimally small $L^{\\infty}$ error. Specifically, given a rational function with $n$ poles in the unit disk, a rational approximation with $m\\ll n$ poles in the unit disk may be obtained from the $m$th con-eigenvector of an $n\\times n$ Cauchy matrix, where the associated con-eigenvalue $\\lambda_{m}>0$ gives the approximation error in the $L^{\\infty}$ norm. Unfortunately, standard algorithms do not accurately "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3196","kind":"arxiv","version":7},"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"}