{"paper":{"title":"Estimates on Neumann eigenfunctions at the boundary, and the \"Method of Particular Solutions\" for computing them","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.NA"],"primary_cat":"math.SP","authors_text":"A. H. Barnett, Andrew Hassell","submitted_at":"2011-07-12T00:31:28Z","abstract_excerpt":"We consider the \"Method of particular solutions\" for numerically computing eigenvalues and eigenfunctions of the Laplacian $\\Delta$ on a smooth, bounded domain Omega in RR^n with either Dirichlet or Neumann boundary conditions. This method constructs approximate eigenvalues E, and approximate eigenfunctions u that satisfy $\\Delta u=Eu$ in Omega, but not the exact boundary condition. An inclusion bound is then an estimate on the distance of E from the actual spectrum of the Laplacian, in terms of (boundary data of) u. We prove operator norm estimates on certain operators on $L^2(\\partial \\Omega"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2172","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"}