{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T14:40:08Z","timestamp":1740148808190,"version":"3.37.3"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2024,6,10]],"date-time":"2024-06-10T00:00:00Z","timestamp":1717977600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,6,10]],"date-time":"2024-06-10T00:00:00Z","timestamp":1717977600000},"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":"publisher","award":["12001395"],"award-info":[{"award-number":["12001395"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2024,10]]},"DOI":"10.1007\/s12190-024-02143-y","type":"journal-article","created":{"date-parts":[[2024,6,10]],"date-time":"2024-06-10T06:02:20Z","timestamp":1717999340000},"page":"4519-4536","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A class of ADI method for the nonsymmetric coupled algebraic Riccati equations"],"prefix":"10.1007","volume":"70","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4314-3581","authenticated-orcid":false,"given":"Jinrui","family":"Guan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruiping","family":"Wen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,6,10]]},"reference":[{"key":"2143_CR1","volume-title":"Jump Linear Systems in Automatic Control","author":"M Mariton","year":"1990","unstructured":"Mariton, M.: Jump Linear Systems in Automatic Control. Marcel Dekker, New York (1990)"},{"key":"2143_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8081-7","volume-title":"Matrix Riccati Equations","author":"H Abou-Kandil","year":"2003","unstructured":"Abou-Kandil, H., Freiling, G., Ionescu, V., Jank, G.: Matrix Riccati Equations. Birkh\u00e4user Verlag, Basel (2003)"},{"key":"2143_CR3","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)"},{"issue":"2","key":"2143_CR4","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":"7","key":"2143_CR5","doi-asserted-by":"publisher","first-page":"777","DOI":"10.1109\/9.57016","volume":"35","author":"Y Ji","year":"1990","unstructured":"Ji, Y., Chizeck, H.J.: Controllability, stability, and continuous-time Markovian jump linear quadratic control. IEEE Trans. Autom. Control 35(7), 777\u2013788 (1990)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"11","key":"2143_CR6","doi-asserted-by":"publisher","first-page":"1666","DOI":"10.1109\/9.544005","volume":"41","author":"MA Rami","year":"1996","unstructured":"Rami, M.A., Ghaoui, L.E.: LMI optimization for nonstandard Riccati equations arising in stochastic control. IEEE Trans. Autom. Control 41(11), 1666\u20131671 (1996)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"2","key":"2143_CR7","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1016\/S0167-6911(97)00103-5","volume":"33","author":"RMDV Pessoa","year":"1998","unstructured":"Pessoa, R.M.D.V., Sales, R.M.: On the solution of coupled Riccati equations used in mixed $$H^{2}$$ and $$H^{\\infty }$$ optimal control. Syst. Control Lett. 33(2), 115\u2013124 (1998)","journal-title":"Syst. Control Lett."},{"issue":"10","key":"2143_CR8","doi-asserted-by":"publisher","first-page":"1590","DOI":"10.1109\/TAC.2002.803528","volume":"47","author":"Y Fang","year":"2002","unstructured":"Fang, Y., Loparo, K.A.: Stabilization of continuous-time jump linear systems. IEEE Trans. Autom. Control 47(10), 1590\u20131603 (2002)","journal-title":"IEEE Trans. Autom. Control"},{"key":"2143_CR9","doi-asserted-by":"publisher","first-page":"1088","DOI":"10.1016\/j.automatica.2007.11.001","volume":"44","author":"R Davies","year":"2008","unstructured":"Davies, R., Shi, P., Wiltshire, R.: Upper solution bounds of the continuous and discrete coupled algebraic Riccati equations. Automatica 44, 1088\u20131096 (2008)","journal-title":"Automatica"},{"issue":"4","key":"2143_CR10","doi-asserted-by":"publisher","first-page":"726","DOI":"10.1080\/00207179.2011.573001","volume":"84","author":"J Zhang","year":"2011","unstructured":"Zhang, J., Liu, J.Z.: Upper solution bounds of the continuous coupled algebraic Riccati matrix equation. Int. J. Control 84(4), 726\u2013736 (2011)","journal-title":"Int. J. Control"},{"issue":"8","key":"2143_CR11","doi-asserted-by":"publisher","first-page":"1430","DOI":"10.1080\/00207179.2011.604794","volume":"84","author":"JZ Liu","year":"2011","unstructured":"Liu, J.Z., Zhang, J.: The existence uniqueness and the fixed iterative algorithm of the solution for the discrete coupled algebraic Riccati equation. Int. J. Control 84(8), 1430\u20131441 (2011)","journal-title":"Int. J. Control"},{"issue":"4","key":"2143_CR12","first-page":"1135","volume":"34","author":"J Zhang","year":"2017","unstructured":"Zhang, J., Liu, J.Z., Li, W.: The solution bounds and fixed point iterative algorithm for the discrete coupled algebraic Riccati equation applied to automatic control[J]. IMA J. Math. Control Inform. 34(4), 1135\u20131156 (2017)","journal-title":"IMA J. Math. Control Inform."},{"key":"2143_CR13","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1016\/j.sysconle.2018.09.012","volume":"122","author":"T Zhao","year":"2018","unstructured":"Zhao, T., Zhou, B., Michiels, W.: Stability analysis of linear time-varying time-delay systems by non-quadratic Lyapunov functions with indefinite derivatives. Syst. Control Lett. 122, 77\u201385 (2018)","journal-title":"Syst. Control Lett."},{"issue":"1","key":"2143_CR14","volume":"364","author":"AG Wu","year":"2020","unstructured":"Wu, A.G., Sun, H.J., Zhang, Y.: A novel iterative algorithm for solving coupled Riccati equations. Appl. Math. Comput. 364(1), 124645 (2020)","journal-title":"Appl. Math. Comput."},{"key":"2143_CR15","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1016\/j.apnum.2021.07.001","volume":"170","author":"M Dehghan","year":"2021","unstructured":"Dehghan, M., Shirilord, A.: On the Hermitian and skew-Hermitian splitting-like iteration approach for solving complex continuous-time algebraic Riccati matrix equation[J]. Appl. Numer. Math. 170, 109\u2013127 (2021)","journal-title":"Appl. Numer. Math."},{"key":"2143_CR16","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","key":"2143_CR17","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":"8","key":"2143_CR18","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":"2143_CR19","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":"10","key":"2143_CR20","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."},{"key":"2143_CR21","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."},{"key":"2143_CR22","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1016\/j.apnum.2020.08.001","volume":"158","author":"M Dehghan","year":"2020","unstructured":"Dehghan, M., Shirilord, A.: Matrix multisplitting Picard-iterative method for solving generalized absolute value matrix equation. Appl. Numer. Math. 158, 425\u2013438 (2020)","journal-title":"Appl. Numer. Math."},{"key":"2143_CR23","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2019.112567","volume":"368","author":"LQ Dong","year":"2020","unstructured":"Dong, L.Q., Li, J.C.: 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":"2143_CR24","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1007\/s00366-019-00838-6","volume":"37","author":"M Dehghan","year":"2021","unstructured":"Dehghan, M., Shirilord, A.: Solving complex Sylvester matrix equation by accelerated double-step scale splitting (ADSS) method. Eng. Comput. 37, 489\u2013508 (2021)","journal-title":"Eng. Comput."},{"key":"2143_CR25","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2021.113614","volume":"396","author":"CL Liu","year":"2021","unstructured":"Liu, C.L., Wang, W.G., Xue, J.G., 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."},{"issue":"2","key":"2143_CR26","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1007\/s40314-021-01747-5","volume":"41","author":"M Dehghan","year":"2022","unstructured":"Dehghan, M., Shirilord, A.: Approximating optimal parameters for generalized preconditioned Hermitian and skew-Hermitian splitting (GPHSS) method. Comput. Appl. Math. 41(2), 72 (2022)","journal-title":"Comput. Appl. Math."},{"key":"2143_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2022.108040","volume":"131","author":"A Shirilord","year":"2022","unstructured":"Shirilord, A., Dehghan, M.: Closed-form solution of non-symmetric algebraic Riccati matrix equation. Appl. Math. Lett. 131, 108040 (2022)","journal-title":"Appl. Math. Lett."},{"key":"2143_CR28","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)"},{"key":"2143_CR29","volume-title":"Matrix Analysis and Applied Linear Algebra","author":"CD Meyer","year":"2003","unstructured":"Meyer, C.D., Stewart, I.: Matrix Analysis and Applied Linear Algebra. SIAM, Philadelphia (2003)"},{"key":"2143_CR30","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1007\/s40314-020-01143-5","volume":"39","author":"JZ Liu","year":"2020","unstructured":"Liu, J.Z., Zhang, J., Luo, F.F.: Newton\u2019s method for the positive solution of the coupled algebraic Riccati equation applied to automatic control. Comput. Appl. Math. 39, 113 (2020)","journal-title":"Comput. Appl. Math."},{"issue":"6","key":"2143_CR31","doi-asserted-by":"publisher","first-page":"4119","DOI":"10.1007\/s12190-021-01697-5","volume":"68","author":"J Zhang","year":"2022","unstructured":"Zhang, J., Liu, J., Luo, F.: A class of fixed point iteration for the coupled algebraic Riccati equation. J. Appl. Math Comput. 68(6), 4119\u20134133 (2022)","journal-title":"J. Appl. Math Comput."},{"issue":"1","key":"2143_CR32","doi-asserted-by":"publisher","first-page":"374","DOI":"10.1002\/asjc.2205","volume":"23","author":"J Zhang","year":"2021","unstructured":"Zhang, J., Tan, F.Y.: Numerical methods for the minimal non-negative solution of the non-symmetric coupled algebraic Riccati equation. Asian J. Control 23(1), 374\u2013386 (2021)","journal-title":"Asian J. Control"},{"key":"2143_CR33","doi-asserted-by":"publisher","first-page":"198","DOI":"10.1137\/0116017","volume":"16","author":"RA Smith","year":"1968","unstructured":"Smith, R.A.: Matrix equation $$XA + BX = C$$. SIAM J. Appl. Math. 16, 198\u2013201 (1968)","journal-title":"SIAM J. Appl. Math."}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-024-02143-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-024-02143-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-024-02143-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,26]],"date-time":"2024-09-26T12:28:13Z","timestamp":1727353693000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-024-02143-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,10]]},"references-count":33,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2024,10]]}},"alternative-id":["2143"],"URL":"https:\/\/doi.org\/10.1007\/s12190-024-02143-y","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"type":"print","value":"1598-5865"},{"type":"electronic","value":"1865-2085"}],"subject":[],"published":{"date-parts":[[2024,6,10]]},"assertion":[{"value":"27 February 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 May 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 May 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 June 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not Applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}]}}