{"paper":{"title":"A mechanism of three-dimensional quadratic termination for the gradient method with applications","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Xin-Wei Liu, Yakui Huang, Yu-Hong Dai","submitted_at":"2022-12-14T14:44:20Z","abstract_excerpt":"Recent studies show that the two-dimensional quadratic termination property has great potential in improving performance of the gradient method. However, it is not clear whether higher-dimensional quadratic termination leads further benefits. In this paper, we provide an affirmative answer by introducing a mechanism of three-dimensional quadratic termination for the gradient method. A novel stepsize is derived from the mechanism such that a family of delayed gradient methods equipping with the novel stepsize have the three-dimensional quadratic termination property. When applied to the Barzila"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.07255","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.07255/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}