{"paper":{"title":"A Revisit of Block Power Methods for Finite State Markov Chain Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.NA","authors_text":"Hao Ji, Seth H. Weinberg, Yaohang Li","submitted_at":"2016-10-27T16:55:27Z","abstract_excerpt":"In this paper, we revisit the generalized block power methods for approximating the eigenvector associated with $\\lambda_1 = 1$ of a Markov chain transition matrix. Our analysis of the block power method shows that when $s$ linearly independent probability vectors are used as the initial block, the convergence of the block power method to the stationary distribution depends on the magnitude of the $(s+1)$th dominant eigenvalue $\\lambda_{s+1}$ of $P$ instead of that of $\\lambda_2$ in the power method. Therefore, the block power method with block size $s$ is particularly effective for transition"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08881","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"}