{"paper":{"title":"A Generalized Fundamental Matrix for Computing Fundamental Quantities of Markov Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY"],"primary_cat":"math.OC","authors_text":"Li Xia, Peter W. Glynn","submitted_at":"2016-04-15T03:25:16Z","abstract_excerpt":"As is well known, the fundamental matrix $(I - P + e \\pi)^{-1}$ plays an important role in the performance analysis of Markov systems, where $P$ is the transition probability matrix, $e$ is the column vector of ones, and $\\pi$ is the row vector of the steady state distribution. It is used to compute the performance potential (relative value function) of Markov decision processes under the average criterion, such as $g=(I - P + e \\pi)^{-1} f$ where $g$ is the column vector of performance potentials and $f$ is the column vector of reward functions. However, we need to pre-compute $\\pi$ before we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04343","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"}