{"paper":{"title":"Some notes on applying computational divided differencing in optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.OC","authors_text":"Stephen Vavasis","submitted_at":"2013-07-15T20:21:43Z","abstract_excerpt":"We consider the problem of accurate computation of the finite difference $f(\\x+\\s)-f(\\x)$ when $\\Vert\\s\\Vert$ is very small. Direct evaluation of this difference in floating point arithmetic succumbs to cancellation error and yields 0 when $\\s$ is sufficiently small. Nonetheless, accurate computation of this finite difference is required by many optimization algorithms for a \"sufficient decrease\" test. Reps and Rall proposed a programmatic transformation called \"computational divided differencing\" reminiscent of automatic differentiation to compute these differences with high accuracy. The run"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4097","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"}