{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:35:59Z","timestamp":1787322959886,"version":"3.56.0"},"reference-count":10,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[1996,10]]},"abstract":"<jats:p>An upper bound is given for the projective distance $d( Y( k ),V ( k ) )$, where $Y( k ) = A( k )Y( k - 1 )$ is a nonautonomous linear process in the positive quadrant of $\\mathbb{R}^n$($A( i )$ irreducible for all i) and the $V( i )$\u2019s are the Perron vectors of the $A( i )$\u2019s. This bound shows that the larger k is, and the more slowly the Perron vectors have varied in the recent past preceding k, the smaller the distance $d ( Y ( k ),V ( k ) )$ will be. Corollaries are given concerning the growth of the $Y( k )$\u2019s and the behavior of the backward product of matrices $A( 1 )A( 2 ) \\cdots A( k )$. The results are illustrated with a numerical simulation. The cases of stochastic matrices and cyclic matrices are investigated.<\/jats:p>","DOI":"10.1137\/s089547989427796x","type":"journal-article","created":{"date-parts":[[2005,2,27]],"date-time":"2005-02-27T07:15:07Z","timestamp":1109488507000},"page":"822-833","source":"Crossref","is-referenced-by-count":3,"title":["On the Dynamics of the Linear Process $Y( k ) = A ( k )Y ( k - 1 )$ with Irreducible Matrices $A( k )$"],"prefix":"10.1137","volume":"17","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(91)90286-6"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(93)00058-8"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.2307\/1426141"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100056176"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176990650"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1017\/S030500410005252X"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/0126026"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(92)90294-K"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/0-387-32792-4"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1963-0154756-3"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S089547989427796X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:35:32Z","timestamp":1787319332000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S089547989427796X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,10]]},"references-count":10,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1996,10]]}},"alternative-id":["10.1137\/S089547989427796X"],"URL":"https:\/\/doi.org\/10.1137\/s089547989427796x","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,10]]}}}