{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,26]],"date-time":"2025-07-26T09:31:28Z","timestamp":1753522288506,"version":"3.37.3"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,11,6]],"date-time":"2023-11-06T00:00:00Z","timestamp":1699228800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,11,6]],"date-time":"2023-11-06T00:00:00Z","timestamp":1699228800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12001395"],"award-info":[{"award-number":["12001395"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"the special fund for Science and Technology Innovation Teams of Shanxi Province","award":["202204051002018"],"award-info":[{"award-number":["202204051002018"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2024,9]]},"DOI":"10.1007\/s11075-023-01695-7","type":"journal-article","created":{"date-parts":[[2023,11,6]],"date-time":"2023-11-06T08:01:53Z","timestamp":1699257713000},"page":"119-134","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A generalized ALI iteration method for nonsymmetric algebraic Riccati equations"],"prefix":"10.1007","volume":"97","author":[{"given":"Jinrui","family":"Guan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhixin","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,11,6]]},"reference":[{"issue":"2","key":"1695_CR1","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1016\/0167-6911(88)90080-1","volume":"11","author":"KM Zhou","year":"1988","unstructured":"Zhou, K.M., Khargonekar, P.P.: An algebraic Riccati equation approach to $$H^{\\infty }$$ optimization. Syst. Control Lett. 11(2), 85\u201391 (1988)","journal-title":"Syst. Control Lett."},{"issue":"2","key":"1695_CR2","doi-asserted-by":"publisher","first-page":"390","DOI":"10.1214\/aoap\/1177005065","volume":"4","author":"LCG Rogers","year":"1994","unstructured":"Rogers, L.C.G.: Fluid models in queueing theory and Wiener-Hopf factorization of Markov chains. Ann. Appl. Probab. 4(2), 390\u2013413 (1994)","journal-title":"Ann. Appl. Probab."},{"issue":"1","key":"1695_CR3","doi-asserted-by":"publisher","first-page":"228","DOI":"10.1137\/S0895479897318253","volume":"20","author":"J Juang","year":"1999","unstructured":"Juang, J., Lin, W.W.: Nonsymmetric algebraic Riccati equations and Hamilton-like matrices. SIAM J. Matrix Anal. Appl. 20(1), 228\u2013243 (1999)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"1","key":"1695_CR4","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1081\/STM-200046511","volume":"21","author":"NG Bean","year":"2005","unstructured":"Bean, N.G., O\u2019Reilly, M.M., Taylor, P.G.: Algorithms for return probabilities for stochastic fluid flows. Stoch. Models 21(1), 149\u2013184 (2005)","journal-title":"Stoch. Models"},{"issue":"3","key":"1695_CR5","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1007\/s11009-008-9077-3","volume":"10","author":"NG Bean","year":"2008","unstructured":"Bean, N.G., O\u2019Reilly, M.M., Taylor, P.G.: Algorithms for the Laplace-Stieltjes transforms of first return times for stochastic fluid flows. Methodol. Comput. Appl. Probab. 10(3), 381\u2013408 (2008)","journal-title":"Methodol. Comput. Appl. Probab."},{"key":"1695_CR6","volume-title":"Numerical methods for linear control systems","author":"B Datta","year":"2004","unstructured":"Datta, B.: Numerical methods for linear control systems. Academic Press, New York (2004)"},{"key":"1695_CR7","volume-title":"Numerical solution of algebraic Riccati equations","author":"DA Bini","year":"2012","unstructured":"Bini, D.A., Iannazzo, B., Meini, B.: Numerical solution of algebraic Riccati equations. SIAM, Philadelphia (2012)"},{"issue":"1\u20133","key":"1695_CR8","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1016\/S0024-3795(02)00431-7","volume":"357","author":"CH Guo","year":"2002","unstructured":"Guo, C.H.: A note on the minimal nonnegative solution of a nonsymmetric algebraic Riccati equation. Linear Algebra Appl. 357(1\u20133), 299\u2013302 (2002)","journal-title":"Linear Algebra Appl."},{"issue":"10","key":"1695_CR9","doi-asserted-by":"publisher","first-page":"2800","DOI":"10.1016\/j.laa.2013.08.018","volume":"439","author":"CH Guo","year":"2013","unstructured":"Guo, C.H.: On algebraic Riccati equations associated with M-matrices. Linear Algebra Appl. 439(10), 2800\u20132814 (2013)","journal-title":"Linear Algebra Appl."},{"issue":"1","key":"1695_CR10","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1137\/S0895479800375680","volume":"23","author":"CH Guo","year":"2001","unstructured":"Guo, C.H.: Nonsymmetric algebraic Riccati equations and Wiener-Hopf factorization for M-matrices. SIAM J. Matrix Anal. Appl. 23(1), 225\u2013242 (2001)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"2","key":"1695_CR11","doi-asserted-by":"publisher","first-page":"376","DOI":"10.1137\/S089547989834980X","volume":"22","author":"CH Guo","year":"2000","unstructured":"Guo, C.H., Laub, A.J.: On the iterative solution of a class of nonsymmetric algebraic Riccati equation. SIAM J. Matrix Anal. Appl. 22(2), 376\u2013391 (2000)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"2","key":"1695_CR12","doi-asserted-by":"publisher","first-page":"396","DOI":"10.1137\/050647669","volume":"29","author":"CH Guo","year":"2007","unstructured":"Guo, C.H., Higham, N.J.: Iterative solution of a nonsymmetric algebraic Riccati equation. SIAM J. Matrix Anal. Appl. 29(2), 396\u2013412 (2007)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"8","key":"1695_CR13","doi-asserted-by":"publisher","first-page":"655","DOI":"10.1002\/nla.500","volume":"13","author":"ZZ Bai","year":"2006","unstructured":"Bai, Z.Z., Guo, X.X., Xu, S.F.: Alternately linearized implicit iteration methods for the minimal nonnegative solutions of the nonsymmetric algebraic Riccati equations. Numer. Linear Algebra Appl. 13(8), 655\u2013674 (2006)","journal-title":"Numer. Linear Algebra Appl."},{"issue":"3","key":"1695_CR14","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1007\/s00211-005-0673-7","volume":"103","author":"XX Guo","year":"2006","unstructured":"Guo, X.X., Lin, W.W., Xu, S.F.: A structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equation. Numer. Math. 103(3), 393\u2013412 (2006)","journal-title":"Numer. Math."},{"issue":"4","key":"1695_CR15","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1007\/s00211-010-0319-2","volume":"116","author":"DA Bini","year":"2010","unstructured":"Bini, D.A., Meini, B., Poloni, F.: Transforming algebraic Riccati equations into unilateral quadratic matrix equations. Numer. Math. 116(4), 553\u2013578 (2010)","journal-title":"Numer. Math."},{"issue":"1","key":"1695_CR16","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1137\/110835463","volume":"33","author":"WG Wang","year":"2012","unstructured":"Wang, W.G., Wang, W.C., Li, R.C.: Alternating-directional doubling algorithm for M-matrix algebraic Riccati equations. SIAM J. Matrix Anal. Appl. 33(1), 170\u2013194 (2012)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"4","key":"1695_CR17","doi-asserted-by":"publisher","first-page":"1083","DOI":"10.1137\/060660837","volume":"29","author":"CH Guo","year":"2008","unstructured":"Guo, C.H., Iannazzo, B., Meini, B.: On the doubling algorithm for a (shift) algebraic Riccati equation. SIAM J. Matrix Anal. Appl. 29(4), 1083\u20131100 (2008)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"15","key":"1695_CR18","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1016\/j.laa.2015.11.024","volume":"493","author":"CH Guo","year":"2016","unstructured":"Guo, C.H., Lu, D.: On algebraic Riccati equations associated with regular singular M-matrices. Linear Algebra Appl. 493(15), 108\u2013119 (2016)","journal-title":"Linear Algebra Appl."},{"issue":"2","key":"1695_CR19","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1002\/nla.2025","volume":"23","author":"TM Huang","year":"2016","unstructured":"Huang, T.M., Huang, W.Q., Li, R.C., Lin, W.W.: A new two-phase structure-preserving doubling algorithm for critically singular M-matrix algebraic Riccati equations. Numer. Linear Algebra Appl. 23(2), 291\u2013313 (2016)","journal-title":"Numer. Linear Algebra Appl."},{"key":"1695_CR20","doi-asserted-by":"publisher","first-page":"733","DOI":"10.1007\/s00211-016-0815-0","volume":"135","author":"JG Xue","year":"2017","unstructured":"Xue, J.G., Li, R.C.: Highly accurate doubling algorithms for M-matrix algebraic Riccati equations. Numer. Math. 135, 733\u2013767 (2017)","journal-title":"Numer. Math."},{"issue":"2","key":"1695_CR21","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1007\/s00211-017-0907-5","volume":"138","author":"P Benner","year":"2018","unstructured":"Benner, P., Bujanovi\u0107, Z., K\u00fcrschner, P., et al.: RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations. Numer. Math. 138(2), 301\u2013330 (2018)","journal-title":"Numer. Math."},{"key":"1695_CR22","doi-asserted-by":"crossref","unstructured":"Dong, L., Li, J., Li, G.: The double deflating technique for irreducible singular M-matrix algebraic Riccati equations in the critical case. Linear Multilinear Algebra, 1466862 (2018)","DOI":"10.1080\/03081087.2018.1466862"},{"key":"1695_CR23","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2019.112567","volume":"368","author":"Dong Liqiang","year":"2020","unstructured":"Liqiang, Dong, Jicheng, Li.: A class of complex nonsymmetric algebraic Riccati equations associated with H-matrix. J. Comput. Appl. Math. 368, 112567 (2020)","journal-title":"J. Comput. Appl. Math."},{"key":"1695_CR24","doi-asserted-by":"publisher","first-page":"113614","DOI":"10.1016\/j.cam.2021.113614","volume":"396","author":"C Liu","year":"2021","unstructured":"Liu, C., Wang, W.G., Xue, J., Li, R.C.: Accurate numerical solution for structured M-matrix algebraic Riccati equations. J. Comput. Appl. Math. 396, 113614 (2021)","journal-title":"J. Comput. Appl. Math."},{"key":"1695_CR25","doi-asserted-by":"publisher","first-page":"113447","DOI":"10.1016\/j.cam.2021.113447","volume":"391","author":"PC Weng","year":"2021","unstructured":"Weng, P.C.: Solving large-scale nonsymmetric algebraic Riccati equations from two-dimensional transport models by doubling. J. Comput. Appl. Math. 391, 113447 (2021)","journal-title":"J. Comput. Appl. Math."},{"key":"1695_CR26","doi-asserted-by":"crossref","unstructured":"Zhang, J., Liu, J., Luo, F.: A class of fixed point iteration for the coupled algebraic Riccati equation. J. Appl. Math Comput., 1\u201315 (2022)","DOI":"10.1007\/s12190-021-01697-5"},{"issue":"1\u20132","key":"1695_CR27","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1007\/s12190-015-0867-9","volume":"50","author":"HZ Lu","year":"2016","unstructured":"Lu, H.Z., Ma, C.F.: A new linearized implicit iteration method for nonsymmetric algebraic Riccati equations. J. Appl. Math. Comput. 50(1\u20132), 227\u2013241 (2016)","journal-title":"J. Appl. Math. Comput."},{"issue":"1","key":"1695_CR28","doi-asserted-by":"publisher","first-page":"54","DOI":"10.4208\/jms.v50n1.17.04","volume":"50","author":"JR Guan","year":"2017","unstructured":"Guan, J.R., Lu, L.Z.: New alternately linearized implicit iteration for M-matrix algebraic Riccati equations. J. Math. Stud. 50(1), 54\u201364 (2017)","journal-title":"J. Math. Stud."},{"key":"1695_CR29","first-page":"442","volume":"347","author":"JR Guan","year":"2019","unstructured":"Guan, J.R.: Modified alternately linearized implicit iteration method for M-matrix algebraic Riccati equations. Appl. Math. Comput. 347, 442\u2013448 (2019)","journal-title":"Appl. Math. Comput."},{"issue":"6","key":"1695_CR30","first-page":"811","volume":"39","author":"JR Guan","year":"2019","unstructured":"Guan, J.R., Zhou, F., Zubair, A.: A modified alternately linearized implicit iteration method for M-matrix algebraic Riccati equation. J. Math. 39(6), 811\u2013822 (2019)","journal-title":"J. Math."},{"key":"1695_CR31","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971262","volume-title":"Nonnegative matrices in the mathematical sciences","author":"A Berman","year":"1994","unstructured":"Berman, A., Plemmons, R.J.: Nonnegative matrices in the mathematical sciences. Academic Press, New York (1994)"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-023-01695-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11075-023-01695-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-023-01695-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,6]],"date-time":"2024-08-06T09:22:17Z","timestamp":1722936137000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11075-023-01695-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,6]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,9]]}},"alternative-id":["1695"],"URL":"https:\/\/doi.org\/10.1007\/s11075-023-01695-7","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"type":"print","value":"1017-1398"},{"type":"electronic","value":"1572-9265"}],"subject":[],"published":{"date-parts":[[2023,11,6]]},"assertion":[{"value":"5 May 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 October 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 November 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"The authors declare no competing interests.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}