{"paper":{"title":"Approximation error of the Lagrange reconstructing polynomial","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":"2010-01-04T13:31:16Z","abstract_excerpt":"The reconstruction approach [Shu C.W.: {\\em SIAM Rev.} {\\bf 51} (2009) 82--126] for the numerical approximation of $f'(x)$ is based on the construction of a dual function $h(x)$ whose sliding averages over the interval $[x-\\tfrac{1}{2}\\Delta x,x+\\tfrac{1}{2}\\Delta x]$ are equal to $f(x)$ (assuming an homogeneous grid of cell-size $\\Delta x$). We study the deconvolution problem [Harten A., Engquist B., Osher S., Chakravarthy S.R.: {\\em J. Comp. Phys.} {\\bf 71} (1987) 231--303] which relates the Taylor polynomials of $h(x)$ and $f(x)$, and obtain its explicit solution, by introducing rational nu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.0509","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"}