{"paper":{"title":"On cluster points of alternating projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.OC","authors_text":"Dominikus Noll, Heinz H. Bauschke","submitted_at":"2013-07-10T08:20:20Z","abstract_excerpt":"Suppose that $A$ and $B$ are closed subsets of a Euclidean space such that $A\\cap B\\neq\\varnothing$, and we aim to find a point in this intersection with the help of the sequences $(a_n)_\\nnn$ and $(b_n)_\\nnn$ generated by the \\emph{method of alternating projections}. It is well known that if $A$ and $B$ are convex, then $(a_n)_\\nnn$ and $(b_n)_\\nnn$ converge to some point in $A\\cap B$. The situation in the nonconvex case is much more delicate. In 1990, Combettes and Trussell presented a dichotomy result that guarantees either convergence to a point in the intersection or a nondegenerate compa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2712","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"}