{"paper":{"title":"Inv-ASKIT: A Parallel Fast Diret Solver for Kernel Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.MS"],"primary_cat":"cs.NA","authors_text":"Bo Xiao, Chenhan D. Yu, George Biros, William B. March","submitted_at":"2016-02-03T17:23:24Z","abstract_excerpt":"We present a parallel algorithm for computing the approximate factorization of an $N$-by-$N$ kernel matrix. Once this factorization has been constructed (with $N \\log^2 N $ work), we can solve linear systems with this matrix with $N \\log N $ work. Kernel matrices represent pairwise interactions of points in metric spaces. They appear in machine learning, approximation theory, and computational physics. Kernel matrices are typically dense (matrix multiplication scales quadratically with $N$) and ill-conditioned (solves can require 100s of Krylov iterations). Thus, fast algorithms for matrix mul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01376","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":""},"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"}