{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T04:18:53Z","timestamp":1787372333023,"version":"build-2736575974"},"reference-count":4,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2003,1]]},"abstract":"<jats:p>\n                    The local coefficient of ergodicity $\\tau(T,Y',w)$ of a nonnegative column-allowable matrix T at a fixed positive vector Y is defined as the supremum of d(X'T,Y'T)\/d(X',Y') for X not colinear to Y and d(X',Y')\\leq w$ (d is the projective distance in the positive quadrant). A near-closed-form expression is given for $\\tau(T,Y',w)$. If T' is scrambling (i.e., no two rows of T' are orthogonal), then for any Y&gt;0, $w &lt; \\infty$ we have $\\tau(T,Y',w)&lt;1$. When Y is a positive left eigenvector of T and X\n                    <jats:sub>o<\/jats:sub>\n                    &gt;0, these results can be used to prove the convergence in direction of X'\n                    <jats:sub>o<\/jats:sub>\n                    T\n                    <jats:sup>p<\/jats:sup>\n                    to Y'. Results are illustrated with a numerical example.\n                  <\/jats:p>","DOI":"10.1137\/s0895479801391801","type":"journal-article","created":{"date-parts":[[2003,10,11]],"date-time":"2003-10-11T19:55:33Z","timestamp":1065902133000},"page":"507-516","source":"Crossref","is-referenced-by-count":1,"title":["The Local Coefficient of Ergodicity of a Nonnegative Matrix"],"prefix":"10.1137","volume":"25","author":[{"given":"Marc","family":"Artzrouni","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(93)00058-8"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479898348969"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511810817"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1007\/0-387-32792-4"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0895479801391801","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:38:07Z","timestamp":1787333887000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0895479801391801"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,1]]},"references-count":4,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2003,1]]}},"alternative-id":["10.1137\/S0895479801391801"],"URL":"https:\/\/doi.org\/10.1137\/s0895479801391801","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,1]]}}}