{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:19:45Z","timestamp":1787321985603,"version":"build-2736575974"},"reference-count":19,"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":[[1996,4]]},"abstract":"<jats:p>Let A be a real weakly diagonally dominant M-matrix. We establish upper and lower bounds for the minimal eigenvalue of A, for its corresponding eigenvector, and for the entries of the inverse of A. Our results are applied to find meaningful two-sided bounds for both the $\\ell _1 $-norm and the weighted Perron-norm of the solution $x ( t )$ to the linear differential system $\\dot x = - Ax,\\, x ( 0 ) = x_0 &gt; 0$. These systems occur in a number of applications, including compartmental analysis and RC electrical circuits. A detailed analysis of a model for the transient behaviour of digital circuits is given to illustrate the theory.<\/jats:p>","DOI":"10.1137\/s0895479894276370","type":"journal-article","created":{"date-parts":[[2005,2,27]],"date-time":"2005-02-27T07:15:07Z","timestamp":1109488507000},"page":"298-312","source":"Crossref","is-referenced-by-count":60,"title":["On Two-Sided Bounds Related to Weakly Diagonally Dominant\n                    <i>M<\/i>\n                    -Matrices with Application to Digital Circuit Dynamics"],"prefix":"10.1137","volume":"17","author":[{"given":"P. N.","family":"Shivakumar","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joseph J.","family":"Williams","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qiang","family":"Ye","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Corneliu A.","family":"Marinov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,2,17]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1002\/sapm1964431117"},{"key":"R2","first-page":"581","volume":"8","author":"Chan P. K.","year":"1989","journal-title":"IEEE Trans. Circuits Systems I Fund. Theory Appl."},{"key":"R3","first-page":"33","volume":"9","author":"Chew Kim Ho","year":"1976","journal-title":"Nanta Math."},{"key":"R4","volume-title":"Stability and asymptotic behavior of differential equations","author":"Coppel W. A.","year":"1965"},{"key":"R5","volume-title":"Principles of Differential and Integral Equations","author":"Corduneanu C.","year":"1988"},{"key":"R6","volume-title":"Design and Analysis of VLSI Circuits","author":"Glasser L. A.","year":"1985"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1972-0294799-8"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1002\/cta.4490180605"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-3440-8"},{"key":"R10","volume-title":"Nonnegative Matrices","author":"Minc H.","year":"1987"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1952-0052380-7"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1109\/43.45867"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1969.tb01105.x"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1974-0332820-0"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1976-059-1"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(75)90112-3"},{"key":"R17","volume-title":"Matrix iterative analysis","author":"Varga Richard S.","year":"1962"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(76)90037-9"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-86405-6"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0895479894276370","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:16:51Z","timestamp":1787318211000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0895479894276370"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,4]]},"references-count":19,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1996,4]]}},"alternative-id":["10.1137\/S0895479894276370"],"URL":"https:\/\/doi.org\/10.1137\/s0895479894276370","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,4]]}}}