{"paper":{"title":"On the Performance of a Novel Class of Linear System Solvers and Comparison with State-of-The-Art Algorithms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Bahman Kalantari, Chun Lau","submitted_at":"2023-04-24T15:25:52Z","abstract_excerpt":"We present a comprehensive computational study of a class of linear system solvers, called {\\it Triangle Algorithm} (TA) and {\\it Centering Triangle Algorithm} (CTA), developed by Kalantari \\cite{kalantari23}. The algorithms compute an approximate solution or minimum-norm solution to $Ax=b$ or $A^TAx=A^Tb$, where $A$ is an $m \\times n$ real matrix of arbitrary rank. The algorithms specialize when $A$ is symmetric positive semi-definite. Based on the description and theoretical properties of TA and CTA from \\cite{kalantari23}, we give an implementation of the algorithms that is easy-to-use for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.12168","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/2304.12168/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"}