{"paper":{"title":"Approximation of the least Rayleigh quotient for degree $p$ homogeneous functionals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Erik Lindgren, Ryan Hynd","submitted_at":"2016-02-15T14:59:41Z","abstract_excerpt":"We present two novel methods for approximating minimizers of the abstract Rayleigh quotient $\\Phi(u)/ \\|u\\|^p$. Here $\\Phi$ is a strictly convex functional on a Banach space with norm $\\|\\cdot\\|$, and $\\Phi$ is assumed to be positively homogeneous of degree $p\\in (1,\\infty)$. Minimizers are shown to satisfy $\\partial \\Phi(u)- \\lambda\\mathcal{J}_p(u)\\ni 0$ for a certain $\\lambda\\in \\mathbb{R}$, where $\\mathcal{J}_p$ is the subdifferential of $\\frac{1}{p}\\|\\cdot\\|^p$. The first approximation scheme is based on inverse iteration for square matrices and involves sequences that satisfy $$ \\partial "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04700","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"}