{"paper":{"title":"Representation of the Lagrange reconstructing polynomial by combination of substencils","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"math.NA","authors_text":"G.A. Gerolymos","submitted_at":"2011-02-15T17:40:30Z","abstract_excerpt":"The Lagrange reconstructing polynomial [Shu C.W.: {\\em SIAM Rev.} {\\bf 51} (2009) 82--126] of a function $f(x)$ on a given set of equidistant ($\\Delta x=\\const$) points $\\bigl\\{x_i+\\ell\\Delta x;\\;\\ell\\in\\{-M_-,...,+M_+\\}\\bigr\\}$ is defined [Gerolymos G.A.: {\\em J. Approx. Theory} {\\bf 163} (2011) 267--305] as the polynomial whose sliding (with $x$) averages on $[x-\\tfrac{1}{2}\\Delta x,x+\\tfrac{1}{2}\\Delta x]$ are equal to the Lagrange interpolating polynomial of $f(x)$ on the same stencil. We first study the fundamental functions of Lagrange reconstruction, show that these polynomials have onl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3136","kind":"arxiv","version":3},"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"}