{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,10]],"date-time":"2024-06-10T19:53:54Z","timestamp":1718049234381},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2019,12,19]],"date-time":"2019-12-19T00:00:00Z","timestamp":1576713600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,12,19]],"date-time":"2019-12-19T00:00:00Z","timestamp":1576713600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2020,3]]},"DOI":"10.1007\/s40314-019-1021-3","type":"journal-article","created":{"date-parts":[[2019,12,19]],"date-time":"2019-12-19T16:03:11Z","timestamp":1576771391000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Convergence of relaxed Newton method for order-convex matrix equations"],"prefix":"10.1007","volume":"39","author":[{"given":"Sang-hyup","family":"Seo","sequence":"first","affiliation":[]},{"given":"Jong-Hyeon","family":"Seo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,12,19]]},"reference":[{"key":"1021_CR1","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1023\/A:1025653200299","volume":"45","author":"AS Alfa","year":"2003","unstructured":"Alfa AS (2003) Combined elapsed time and matrix-analytic method for the discrete time $$GI\/G\/1$$ and $$GI^X\/G\/1$$ systems. Queueing Syst 45:5\u201325","journal-title":"Queueing Syst"},{"issue":"1","key":"1021_CR2","doi-asserted-by":"publisher","first-page":"134","DOI":"10.1214\/aoap\/1034625256","volume":"7","author":"NG Bean","year":"1997","unstructured":"Bean NG, Bright LW, Latouche G, Pearce CEM, Pollett PK, Peter G (1997) Taylor. The quasi-stationary behavior of quasi-birth-and-death processes. Ann Appl Probab 7(1):134\u2013155","journal-title":"Ann Appl Probab"},{"issue":"1","key":"1021_CR3","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1109\/9.654908","volume":"43","author":"P Benner","year":"1998","unstructured":"Benner P, Byers R (1998) An exact line search method for solving generalized continuous-time algebraic Riccati equations. IEEE Trans Automat Control 43(1):101\u2013107","journal-title":"IEEE Trans Automat Control"},{"key":"1021_CR4","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198527688.001.0001","volume-title":"Numerical methods for structured Markov chains","author":"DA Bini","year":"2005","unstructured":"Bini DA, Latouche G, Meini B (2005) Numerical methods for structured Markov chains. Oxford University Press, Oxford"},{"issue":"1","key":"1021_CR5","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1137\/0606005","volume":"6","author":"JB Geoffrey","year":"1985","unstructured":"Geoffrey JB, Johnson CR, Wolkowicz H (1985) Nonnegative solutions of a quadratic matrix equation arising from comparison theorems in ordinary differential equations. SIAM J Algebraic Discrete Methods 6(1):47\u201353","journal-title":"SIAM J Algebraic Discrete Methods"},{"key":"1021_CR6","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1137\/0902014","volume":"2","author":"GJ Davis","year":"1981","unstructured":"Davis GJ (1981) Numerical solution of a quadratic matrix equation. SIAM J Sci Comput 2:164\u2013175","journal-title":"SIAM J Sci Comput"},{"issue":"2","key":"1021_CR7","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1145\/357456.357463","volume":"9","author":"GJ Davis","year":"1983","unstructured":"Davis GJ (1983) Algorithm 598: an algorithm to compute solvent of the matrix equation $$AX^2 + BX + C = 0$$. ACM Trans Math Softw 9(2):246\u2013254","journal-title":"ACM Trans Math Softw"},{"key":"1021_CR8","volume-title":"Matrix polynomials","author":"I Gohberg","year":"1982","unstructured":"Gohberg I, Lancaster P, Rodman L (1982) Matrix polynomials. Academic Press, Amsterdam"},{"issue":"1","key":"1021_CR9","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1137\/S0895479800375680","volume":"23","author":"C-H Guo","year":"2001","unstructured":"Guo C-H (2001) Nonsymmetric algebraic Riccati equations and Wiener-Hopf factorization for M-matrices. SIAM J Matrix Anal Appl 23(1):225\u2013242","journal-title":"SIAM J Matrix Anal Appl"},{"key":"1021_CR10","doi-asserted-by":"publisher","first-page":"396","DOI":"10.1137\/050647669","volume":"29","author":"C-H Guo","year":"2007","unstructured":"Guo C-H, Higham NJ (2007) Iterative solution of a nonsymmetric algebraic Riccati equation. SIAM J Matrix Anal Appl 29:396\u2013412","journal-title":"SIAM J Matrix Anal Appl"},{"issue":"2","key":"1021_CR11","doi-asserted-by":"publisher","first-page":"376","DOI":"10.1137\/S089547989834980X","volume":"22","author":"C-H Guo","year":"2000","unstructured":"Guo C-H, Laub AJ (2000) On the iterative solution of a class of nonsymmetric algebraic Riccati equations. SIAM J Matrix Anal Appl 22(2):376\u2013391","journal-title":"SIAM J Matrix Anal Appl"},{"key":"1021_CR12","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1007\/s00211-005-0673-7","volume":"103","author":"X-X Guo","year":"2006","unstructured":"Guo X-X, Lin W-W, Shu-Fang X (2006) A structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equation. Numer Math 103:393\u2013412","journal-title":"Numer Math"},{"key":"1021_CR13","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511629136","volume-title":"Branching processes: variation, growth, and extinction of populations","author":"P Haccou","year":"2005","unstructured":"Haccou P, Jagers P, Vatutin VA (2005) Branching processes: variation, growth, and extinction of populations. Cambridge University Press, Cambridge"},{"key":"1021_CR14","doi-asserted-by":"publisher","first-page":"2791","DOI":"10.1016\/j.laa.2007.12.024","volume":"428","author":"S Hautphenne","year":"2008","unstructured":"Hautphenne S, Latouche G, Remiche M-A (2008) Newton\u2019s iteration for the extinction probability of a Markovian binary tree. Linear Algebra Appl 428:2791\u20132804","journal-title":"Linear Algebra Appl"},{"issue":"1","key":"1021_CR15","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1007\/s11009-009-9141-7","volume":"13","author":"S Hautphenne","year":"2011","unstructured":"Hautphenne S, Latouche G, Remiche M-A (2011) Algorithmic approach to the extinction probability of branching processes. Methodol Comput Appl Probab 13(1):171\u2013192","journal-title":"Methodol Comput Appl Probab"},{"key":"1021_CR16","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1145\/1168134.1168137","volume":"34","author":"S Hautphenne","year":"2006","unstructured":"Hautphenne S, Leibnitz K, Remiche M-A (2006) Extinction probability in Peer-to-Peer file diffusion. ACM SIGMETRICS Perform Eval Rev 34:3\u20134","journal-title":"ACM SIGMETRICS Perform Eval Rev"},{"issue":"2","key":"1021_CR17","doi-asserted-by":"publisher","first-page":"519","DOI":"10.1239\/jap\/996986760","volume":"38","author":"Q-M He","year":"2001","unstructured":"He Q-M, Neuts MF (2001) On the convergence and limits of certain matrix sequences arising in quasi-birth-and-death Markov chains. J Appl Probab 38(2):519\u2013541","journal-title":"J Appl Probab"},{"key":"1021_CR18","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717778","volume-title":"Functions of matrices: theory and computation","author":"NJ Higham","year":"2008","unstructured":"Higham NJ (2008) Functions of matrices: theory and computation. Society for Industrial and Applied Mathematics, Philadelphia"},{"issue":"4","key":"1021_CR19","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1093\/imanum\/20.4.499","volume":"20","author":"NJ Higham","year":"2000","unstructured":"Higham NJ, Kim H-M (2000) Numerical analysis of a quadratic matrix equation. IMA J Numer Anal 20(4):499\u2013519","journal-title":"IMA J Numer Anal"},{"key":"1021_CR20","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1137\/S0895479899350976","volume":"23","author":"NJ Higham","year":"2001","unstructured":"Higham NJ, Kim H-M (2001) Solving a quadratic matrix equation by Newton\u2019s method with exact line searches. SIAM J Matrix Anal Appl 23:303\u2013316","journal-title":"SIAM J Matrix Anal Appl"},{"key":"1021_CR21","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511810817","volume-title":"Matrix analysis","author":"RA Horn","year":"1985","unstructured":"Horn RA, Johnson CR (1985) Matrix analysis. Cambridge University Press, Cambridge"},{"key":"1021_CR22","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1016\/0024-3795(93)00366-8","volume":"230","author":"J Juang","year":"1995","unstructured":"Juang J (1995) Existence of algebraic matrix Riccati equations arising in transport theory. Linear Algebra Appl 230:89\u2013100","journal-title":"Linear Algebra Appl"},{"issue":"2","key":"1021_CR23","doi-asserted-by":"publisher","first-page":"399","DOI":"10.5831\/HMJ.2008.30.2.399","volume":"30","author":"H-M Kim","year":"2008","unstructured":"Kim H-M (2008) Convergence of Newton\u2019s method for solving a class of quadratic matrix equations. Honam Math J 30(2):399\u2013409","journal-title":"Honam Math J"},{"key":"1021_CR24","doi-asserted-by":"publisher","DOI":"10.1007\/b97371","volume-title":"Branching processes in biology","author":"M Kimmel","year":"2002","unstructured":"Kimmel M, Axelrod DE (2002) Branching processes in biology. Springer-Verlag, New York"},{"key":"1021_CR25","volume-title":"Lambda-matrices and vibrating systems","author":"P Lancaster","year":"1966","unstructured":"Lancaster P (1966) Lambda-matrices and vibrating systems. Pergamon Press, Oxford"},{"key":"1021_CR26","volume-title":"The theory of matrices with applications","author":"P Lancaster","year":"1985","unstructured":"Lancaster P, Tismenetsky M (1985) The theory of matrices with applications, 2nd edn. Academic Press, Amsterdam","edition":"2"},{"key":"1021_CR27","unstructured":"Guy L, Vaidyanathan R (1999) Introduction to matrix analytic methods in stochastic modeling. ASA-SIAM"},{"key":"1021_CR28","doi-asserted-by":"crossref","unstructured":"Ortega JM, Rheinboldt WC (2000) Iterative solution of nonlinear equations in several variables. SIAM","DOI":"10.1137\/1.9780898719468"},{"issue":"4","key":"1021_CR29","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1137\/1016079","volume":"16","author":"G Poole","year":"1974","unstructured":"Poole G, Boullion T (1974) A survey on $$M$$-matrices. SIAM Rev 16(4):419\u2013427","journal-title":"SIAM Rev"},{"issue":"2","key":"1021_CR30","doi-asserted-by":"publisher","first-page":"390","DOI":"10.1214\/aoap\/1177005065","volume":"4","author":"LCG Rogers","year":"1994","unstructured":"Rogers LCG (1994) Fluid models in queueing theory and Wiener-Hopf factorization of Markov chains. Ann Appl Probab 4(2):390\u2013413","journal-title":"Ann Appl Probab"},{"issue":"2","key":"1021_CR31","first-page":"55","volume":"12","author":"JH Seo","year":"2008","unstructured":"Seo JH, Ki H-M, m (2008) Solving matrix polynomials by Newton\u2019s method with exact line searches. J Korean Soc Ind Appl Math 12(2):55\u201368","journal-title":"J Korean Soc Ind Appl Math"},{"key":"1021_CR32","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1016\/j.laa.2013.10.043","volume":"440","author":"J-H Seo","year":"2014","unstructured":"Seo J-H, Kim H-M (2014) Convergence of pure and relaxed Newton methods for solving a matrix polynomial equation arising in stochastic models. Linear Algebra Appl 440:34\u201349","journal-title":"Linear Algebra Appl"},{"issue":"3","key":"1021_CR33","doi-asserted-by":"publisher","first-page":"417","DOI":"10.5831\/HMJ.2013.35.3.417","volume":"35","author":"S-H Seo","year":"2013","unstructured":"Seo S-H, Seo J-H, Kim H-M (2013) Newton\u2019s method for solving a quadratic matrix equation with special coefficiant matrices. Honam Math J 35(3):417\u2013433","journal-title":"Honam Math J"},{"issue":"3","key":"1021_CR34","doi-asserted-by":"publisher","first-page":"406","DOI":"10.1137\/0704037","volume":"4","author":"JS Vandergraft","year":"1967","unstructured":"Vandergraft JS (1967) Newton\u2019s method for convex operators in partially ordered spaces. SIAM J Numer Anal 4(3):406\u2013432","journal-title":"SIAM J Numer Anal"},{"issue":"4","key":"1021_CR35","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1007\/s00211-011-0421-0","volume":"120","author":"J Xue","year":"2012","unstructured":"Xue J, Shufang X, Li R-C (2012) Accurate solutions of $${M}$$-matrix algebraic Riccati equations. Numer Math 120(4):671\u2013700","journal-title":"Numer Math"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-019-1021-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s40314-019-1021-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-019-1021-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,18]],"date-time":"2020-12-18T00:35:37Z","timestamp":1608251737000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s40314-019-1021-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,19]]},"references-count":35,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,3]]}},"alternative-id":["1021"],"URL":"https:\/\/doi.org\/10.1007\/s40314-019-1021-3","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,12,19]]},"assertion":[{"value":"2 June 2016","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 December 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 December 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 December 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"39"}}