{"paper":{"title":"Superfast Tikhonov Regularization of Toeplitz Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"(2) Georgia Institute of Technology, Christopher Turnes (1), Computer Engineering, Doru Balcan (2), Justin Romberg (1) ((1) Georgia Institute of Technology, School of Electrical, School of Interactive Computing)","submitted_at":"2013-02-25T22:49:39Z","abstract_excerpt":"Toeplitz-structured linear systems arise often in practical engineering problems. Correspondingly, a number of algorithms have been developed that exploit Toeplitz structure to gain computational efficiency when solving these systems. The earliest \"fast\" algorithms for Toeplitz systems required O(n^2) operations, while more recent \"superfast\" algorithms reduce the cost to O(n (log n)^2) or below. In this work, we present a superfast algorithm for Tikhonov regularization of Toeplitz systems. Using an \"extension-and-transformation\" technique, our algorithm translates a Tikhonov-regularized Toepl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6945","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"}