{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:56:56Z","timestamp":1760245016645},"reference-count":19,"publisher":"Elsevier BV","issue":"2-3","license":[{"start":{"date-parts":[[2000,2,1]],"date-time":"2000-02-01T00:00:00Z","timestamp":949363200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Mathematics and Computation"],"published-print":{"date-parts":[[2000,2]]},"DOI":"10.1016\/s0096-3003(98)10133-9","type":"journal-article","created":{"date-parts":[[2003,4,4]],"date-time":"2003-04-04T22:33:30Z","timestamp":1049495610000},"page":"77-83","source":"Crossref","is-referenced-by-count":21,"title":["The Drazin inverse of updating of a square matrix with application to perturbation formula"],"prefix":"10.1016","volume":"108","author":[{"given":"Yimin","family":"Wei","sequence":"first","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0096-3003(98)10133-9_BIB1","unstructured":"S.L. Campbell, C.D. Meyer, Generalized Inverses of Linear Transformations, Pitman, London, 1979; Dover, New York, 1991"},{"key":"10.1016\/S0096-3003(98)10133-9_BIB2","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1080\/00949658008810405","article-title":"Updating finite Markov chains by using techniques of group matrix inversion","volume":"11","author":"Meyer","year":"1980","journal-title":"J. Statist. Comput. Simul."},{"key":"10.1016\/S0096-3003(98)10133-9_BIB3","unstructured":"J.M. Shoaf, The Drazin inverse of a rank-one modificaiton of a square matrix, Ph.D. Dissertation, North Carolina State University, NC 1975"},{"key":"10.1016\/S0096-3003(98)10133-9_BIB4","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/0024-3795(75)90097-X","article-title":"Continuity properties of the Drazin inverse","volume":"10","author":"Campbell","year":"1975","journal-title":"Linear Algebra Appl."},{"key":"10.1016\/S0096-3003(98)10133-9_BIB5","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/BF01404464","article-title":"On the solution of singular linear systems of algebraic equations by semiitertive methods","volume":"53","author":"Eiermann","year":"1988","journal-title":"Numer. Math."},{"key":"10.1016\/S0096-3003(98)10133-9_BIB6","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1002\/nla.1680010406","article-title":"On the use of two QMR algorithms for solving singular systems and applications in Markov chain modeling","volume":"1","author":"Freund","year":"1994","journal-title":"Numerical Linear Algebra Appl."},{"key":"10.1016\/S0096-3003(98)10133-9_BIB7","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1137\/0607031","article-title":"Using the QR factorization and group inversion to compute, differentiate, and estimate the sensitivity of stationary probabilities for Markov chains","volume":"7","author":"Golub","year":"1986","journal-title":"SIAM J. Alg. Disc. Meth."},{"key":"10.1016\/S0096-3003(98)10133-9_BIB8","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1137\/S0895479890182545","article-title":"Iterative consistency: a concept for the solution of singular systems of linear equations","volume":"15","author":"Hanke","year":"1994","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"10.1016\/S0096-3003(98)10133-9_BIB9","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1080\/0161-118191855850","article-title":"Applications of the Drazin inverse to the hill cryptographic system Part III","volume":"5","author":"Hartwig","year":"1981","journal-title":"Cryptologia"},{"key":"10.1016\/S0096-3003(98)10133-9_BIB10","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/0024-3795(93)90242-G","article-title":"Finite precision behavior of stationary iteration for solving singular systems","volume":"192","author":"Higham","year":"1993","journal-title":"Linear Algebra Appl."},{"key":"10.1016\/S0096-3003(98)10133-9_BIB11","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1137\/1017044","article-title":"The role of the group generalized inverse in the theory of finite Markov chains","volume":"17","author":"Meyer","year":"1975","journal-title":"SIAM Review"},{"key":"10.1016\/S0096-3003(98)10133-9_BIB12","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1137\/0601031","article-title":"The condition number of a finite Markov chains and perturbation bounds for the limiting probabilities","volume":"1","author":"Meyer","year":"1980","journal-title":"SIAM J. Alg. Disc. Meth."},{"key":"10.1016\/S0096-3003(98)10133-9_BIB13","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1007\/BF01388703","article-title":"The Drazin inverse in multibody system dynamics","volume":"64","author":"Simeon","year":"1993","journal-title":"Numer. Math."},{"key":"10.1016\/S0096-3003(98)10133-9_BIB14","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/S0024-3795(96)00159-0","article-title":"The perturbation theory for the Drazin inverse and its applications","volume":"258","author":"Wei","year":"1997","journal-title":"Linear Algebra Appl."},{"key":"10.1016\/S0096-3003(98)10133-9_BIB15","doi-asserted-by":"crossref","first-page":"744","DOI":"10.1137\/S0895479895280697","article-title":"A Characterization and representation of the Drazin inverse","volume":"17","author":"Wei","year":"1996","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"10.1016\/S0096-3003(98)10133-9_BIB16","doi-asserted-by":"crossref","unstructured":"Y. Wei, Index splitting method for the Drazin inverse and the singular linear system, Applied Mathematics and Computation, 95 (1998) 115\u2013124","DOI":"10.1016\/S0096-3003(97)10098-4"},{"key":"10.1016\/S0096-3003(98)10133-9_BIB17","doi-asserted-by":"crossref","unstructured":"Y. Wei, On the perturbation of the group inverse and oblique projection, Applied Mathematics and Computation, 98 (1998) 29\u201342","DOI":"10.1016\/S0096-3003(97)10151-5"},{"key":"10.1016\/S0096-3003(98)10133-9_BIB18","unstructured":"Y. Wei, Solving singular linear system and generalized inverses, Ph.D Thesis, Institute of Mathematics, Fudan University, Shanghai, March, 1997"},{"key":"10.1016\/S0096-3003(98)10133-9_BIB19","doi-asserted-by":"crossref","unstructured":"Y. Wei, Successive matrix squarring algorithm for computing the Drazin inverse, Applied Mathematics and Computation, 108 (2000) 67\u201375","DOI":"10.1016\/S0096-3003(98)10118-2"}],"container-title":["Applied Mathematics and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0096300398101339?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0096300398101339?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,4,12]],"date-time":"2019-04-12T06:22:40Z","timestamp":1555050160000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0096300398101339"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,2]]},"references-count":19,"journal-issue":{"issue":"2-3","published-print":{"date-parts":[[2000,2]]}},"alternative-id":["S0096300398101339"],"URL":"https:\/\/doi.org\/10.1016\/s0096-3003(98)10133-9","relation":{},"ISSN":["0096-3003"],"issn-type":[{"value":"0096-3003","type":"print"}],"subject":[],"published":{"date-parts":[[2000,2]]}}}