{"paper":{"title":"Approximation by short exponential sums with geometric error decay based on Gauss quadrature","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Annie Cuyt, Gerlind Plonka, Yannick Riebe","submitted_at":"2026-06-02T16:31:33Z","abstract_excerpt":"We present new short exponential sum approximations of length $N$ for $f_1(x)=\\frac{1}{a+x}$ with $a>0$ on $[0, \\infty)$ and for $f_2(x)= {\\mathrm e}^{-x^2/2\\sigma}$ with $\\sigma>0$ on ${\\mathbb R}$ with geometric error decay ${\\rho}^{-2N}$\n  for user-defined $N \\ge 2$ and $\\rho >1$. The approximations are built over consecutive intervals $[b_j, \\, b_{j+1}) \\subset [0, \\infty)$, $j \\in {\\mathbb N}_{0}$, with interval lengths that depend on $\\rho$ and grow exponentially for $f_1$ and are equidistant for $f_2$. All parameters determining the exponential sum approximations on $[b_j, \\, b_{j+1})$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03855","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.03855/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"}