{"paper":{"title":"Rigorous numerics for nonlinear operators with tridiagonal dominant linear part","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA"],"primary_cat":"math.DS","authors_text":"Jean-Philippe Lessard, Laurent Desvillettes, Maxime Breden","submitted_at":"2015-03-21T15:45:18Z","abstract_excerpt":"We present a method designed for computing solutions of infinite dimensional non linear operators $f(x) = 0$ with a tridiagonal dominant linear part. We recast the operator equation into an equivalent Newton-like equation $x = T(x) = x - Af(x)$, where $A$ is an approximate inverse of the derivative $Df(\\overline x)$ at an approximate solution $\\overline x$. We present rigorous computer-assisted calculations showing that $T$ is a contraction near $\\overline x$, thus yielding the existence of a solution. Since $Df(\\overline x)$ does not have an asymptotically diagonal dominant structure, the com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06315","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"}