{"paper":{"title":"Least-Squares Pad\\'e approximation of parametric and stochastic Helmholtz maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Davide Pradovera, Fabio Nobile, Francesca Bonizzoni, Ilaria Perugia","submitted_at":"2018-05-14T07:26:13Z","abstract_excerpt":"The present work deals with the rational model order reduction method based on the single-point Least-Square (LS) Pad\\'e approximation technique introduced in [3]. Algorithmical aspects concerning the construction of the rational LS-Pad\\'e approximant are described. In particular, the computation of the Pad\\'e denominator is reduced to the calculation of the eigenvector corresponding to the minimal eigenvalue of a Gramian matrix. The LS-Pad\\'e technique is employed to approximate the frequency response map associated to various parametric time-harmonic wave problems, namely, a transmission/ref"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05031","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":""},"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"}