{"paper":{"title":"Interpolation of scattered data in $\\mathbb{R}^3$ using minimum $L_p$-norm networks, $1<p<\\infty$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Krassimira Vlachkova","submitted_at":"2019-02-19T20:08:10Z","abstract_excerpt":"We consider the extremal problem of interpolation of scattered data in $\\mathbb{R}^3$ by smooth curve networks with minimal $L_p$-norm of the second derivative for $1<p<\\infty$. The problem for $p=2$ was set and solved by Nielson (1983). Andersson et al. (1995) gave a new proof of Nielson's result by using a different approach. Partial results for the problem for $1<p<\\infty$ were announced without proof in (Vlachkova (1992)). Here we present a complete characterization of the solution for $1<p<\\infty$. Numerical experiments are visualized and presented to illustrate and support our results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.07264","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/1902.07264/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"}