{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T02:52:06Z","timestamp":1773370326022,"version":"3.50.1"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2017,4,3]],"date-time":"2017-04-03T00:00:00Z","timestamp":1491177600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11371243"],"award-info":[{"award-number":["11371243"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2018,2]]},"DOI":"10.1007\/s11075-017-0323-z","type":"journal-article","created":{"date-parts":[[2017,4,3]],"date-time":"2017-04-03T16:35:40Z","timestamp":1491237340000},"page":"451-478","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["An improved block splitting preconditioner for complex symmetric indefinite linear systems"],"prefix":"10.1007","volume":"77","author":[{"given":"Ju-Li","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hong-Tao","family":"Fan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chuan-Qing","family":"Gu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,4,3]]},"reference":[{"key":"323_CR1","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1002\/1099-1506(200005)7:4<197::AID-NLA194>3.0.CO;2-S","volume":"7","author":"O Axelsson","year":"2000","unstructured":"Axelsson, O., Kucherov, A.: Real valued iterative methods for solving complex symmetric linear systems. Numer. Linear Algebra Appl. 7, 197\u2013218 (2000)","journal-title":"Numer. Linear Algebra Appl."},{"key":"323_CR2","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1137\/S0895479801395458","volume":"24","author":"Z-Z Bai","year":"2003","unstructured":"Bai, Z.-Z., Golub, G.H., Ng, M.K.: Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems. SIAM J. Matrix Anal. Appl. 24, 603\u2013626 (2003)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"323_CR3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00211-004-0521-1","volume":"98","author":"Z-Z Bai","year":"2004","unstructured":"Bai, Z.-Z., Golub, G.H., Pan, J.-Y.: Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems. Numer. Math. 98, 1\u201332 (2004)","journal-title":"Numer. Math."},{"key":"323_CR4","first-page":"844","volume":"26","author":"Z-Z Bai","year":"2005","unstructured":"Bai, Z.-Z., Golub, G.H., Lu, L.-Z., Yin, J.-F.: Block triangular and skew-Hermitian splitting methods for positive-definite linear systems. SIAM. J. Sci. Comput. 26, 844\u2013863 (2005)","journal-title":"J. Sci. Comput."},{"key":"323_CR5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/imanum\/drl017","volume":"27","author":"Z-Z Bai","year":"2007","unstructured":"Bai, Z.-Z., Golub, G.H.: Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems. IMA. J. Numer. Anal. 27, 1\u201323 (2007)","journal-title":"J. Numer. Anal."},{"key":"323_CR6","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/s00607-010-0077-0","volume":"87","author":"Z-Z Bai","year":"2010","unstructured":"Bai, Z.-Z., Benzi, M., Chen, F.: Modified HSS iteration methods for a class of complex symmetric linear systems. Computing 87, 93\u2013111 (2010)","journal-title":"Computing"},{"key":"323_CR7","doi-asserted-by":"crossref","first-page":"1339","DOI":"10.1007\/s11425-008-0106-z","volume":"51","author":"Z-Z Bai","year":"2008","unstructured":"Bai, Z.-Z.: Several splittings for non-Hermitian linear systems. Sci. China Ser. A: Math. 51, 1339\u20131348 (2008)","journal-title":"Sci. China Ser. A: Math."},{"key":"323_CR8","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/s11075-010-9441-6","volume":"56","author":"Z-Z Bai","year":"2011","unstructured":"Bai, Z.-Z., Benzi, M., Chen, F.: On preconditioned MHSS iteration methods for complex symmetric linear systems. Numer. Algor. 56, 297\u2013317 (2011)","journal-title":"Numer. Algor."},{"key":"323_CR9","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1007\/s00607-010-0125-9","volume":"91","author":"Z-Z Bai","year":"2011","unstructured":"Bai, Z.-Z.: Block preconditioners for elliptic PDE-constrained optimization problems. Computing. 91, 379\u2013395 (2011)","journal-title":"Computing."},{"key":"323_CR10","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1093\/imanum\/drs001","volume":"33","author":"Z-Z Bai","year":"2013","unstructured":"Bai, Z.-Z., Benzi, M., Chen, F., Wang, Z.-Q.: Preconditioned MHSS iteration methods for a class of block two-by-two linear systems with application to distributed control problems. IMA J. Numer. Anal. 33, 343\u2013369 (2013)","journal-title":"IMA J. Numer. Anal."},{"key":"323_CR11","doi-asserted-by":"crossref","first-page":"2523","DOI":"10.1007\/s11425-013-4695-9","volume":"56","author":"Z-Z Bai","year":"2013","unstructured":"Bai, Z.-Z.: Rotated block triangular preconditioning based on PMHSS. Sci. China Math. 56, 2523\u20132538 (2013)","journal-title":"Sci. China Math."},{"key":"323_CR12","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/s10665-013-9670-5","volume":"93","author":"Z-Z Bai","year":"2015","unstructured":"Bai, Z.-Z.: On preconditioned iteration methods for complex linear systems. J. Eng. Math. 93, 41\u201360 (2015)","journal-title":"J. Eng. Math."},{"key":"323_CR13","doi-asserted-by":"crossref","first-page":"598","DOI":"10.1093\/imanum\/drm039","volume":"28","author":"M Benzi","year":"2008","unstructured":"Benzi, M., Bertaccini, D.: Block preconditioning of real-valued iterative algorithms for complex linear systems. IMA. J. Numer. Anal. 28, 598\u2013618 (2008)","journal-title":"J. Numer. Anal."},{"key":"323_CR14","first-page":"36","volume":"58","author":"H-T Fan","year":"2015","unstructured":"Fan, H.-T., Zhu, X.-Y.: A generalized relaxed positive-definite and skew-Hermitian splitting preconditioner for non-Hermitian saddle point problems. Appl. Math. Comput. 58, 36\u201348 (2015)","journal-title":"Appl. Math. Comput."},{"key":"323_CR15","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.aml.2015.11.011","volume":"55","author":"H-T Fan","year":"2016","unstructured":"Fan, H.-T., Zhu, X.-Y.: A modified relaxed splitting preconditioner for generalized saddle point problems from the incompressible Navier-Stokes equations. Appl. Math. Lett. 55, 18\u201326 (2016)","journal-title":"Appl. Math. Lett."},{"key":"323_CR16","unstructured":"Golub, G.H., Van Loan, C.F.: Matrix computations, 3rd edn. The Johns Hopkins University Press , (1996)"},{"key":"323_CR17","doi-asserted-by":"crossref","first-page":"2076","DOI":"10.1137\/S1064827500375096","volume":"24","author":"GH Golub","year":"2003","unstructured":"Golub, G.H., Greif, C.: On solving block-structured indefinite linear systems. SIAM J. Sci. Comput. 24, 2076\u20132092 (2003)","journal-title":"SIAM J. Sci. Comput."},{"key":"323_CR18","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/s10665-013-9674-1","volume":"93","author":"C Lang","year":"2015","unstructured":"Lang, C., Ren, Z.-R.: Inexact rotated block triangular preconditioners for a class of block two-by-two matrices. J. Eng. Math. 93, 87\u201398 (2015)","journal-title":"J. Eng. Math."},{"key":"323_CR19","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1007\/s11075-013-9748-1","volume":"66","author":"X Li","year":"2014","unstructured":"Li, X., Yang, A.-L., Wu, Y.-J.: Lopsided PMHSS iteration method for a class of complex symmetric linear systems. Numer. Algor. 66, 555\u2013568 (2014)","journal-title":"Numer. Algor."},{"key":"323_CR20","first-page":"762","volume":"72","author":"J-Y Pan","year":"2006","unstructured":"Pan, J.-Y., Ng, M.K., Bai, Z.-Z.: New preconditioners for saddle point problems. Appl. Math. Comput. 72, 762\u2013771 (2006)","journal-title":"Appl. Math. Comput."},{"key":"323_CR21","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1137\/100796364","volume":"33","author":"M Pennacchio","year":"2011","unstructured":"Pennacchio, M., Simoncini, V.: Fast structured AMG preconditioning for the bidomain model in electrocardiology. SIAM J. Sci. Comput. 33, 721\u2013745 (2011)","journal-title":"SIAM J. Sci. Comput."},{"key":"323_CR22","doi-asserted-by":"crossref","first-page":"856","DOI":"10.1137\/0907058","volume":"7","author":"Y Saad","year":"1986","unstructured":"Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7, 856\u2013869 (1986)","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"323_CR23","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898718003","volume-title":"Iterative Methods for Sparse Linear Systems","author":"Y Saad","year":"2003","unstructured":"Saad, Y.: Iterative Methods for Sparse Linear Systems, 2nd edn. SIAM, Philadelphia (2003)","edition":"2"},{"key":"323_CR24","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1002\/nla.1952","volume":"22","author":"S-L Wu","year":"2015","unstructured":"Wu, S.-L.: Several variants of the Hermitian and skew-Hermitian splittingmethod for a class of complex symmetric linear systems. Numer. Linear Algebra Appl. 22, 338\u2013356 (2015)","journal-title":"Numer. Linear Algebra Appl."},{"key":"323_CR25","first-page":"468","volume":"249","author":"J-L Zhang","year":"2014","unstructured":"Zhang, J.-L., Gu, C.-Q., Zhang, K.: A relaxed positive-definite and skew-Hermitian splitting preconditioner for saddle point problems. Appl. Math. Comput. 249, 468\u2013479 (2014)","journal-title":"Appl. Math. Comput."},{"key":"323_CR26","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1007\/s10543-015-0590-9","volume":"56","author":"J-L Zhang","year":"2016","unstructured":"Zhang, J.-L., Gu, C.-Q.: A variant of the deteriorated PSS preconditioner for nonsymmetric saddle point problems. BIT Numer. Math. 56, 587\u2013604 (2016)","journal-title":"BIT Numer. Math."},{"key":"323_CR27","doi-asserted-by":"publisher","unstructured":"Zhang, J.-H., Dai, H.: A new block preconditioner for complex symmetric indefinite linear systems. Numer. Algor. doi:\n                        10.1007\/s11075-016-0175-y","DOI":"10.1007\/s11075-016-0175-y"},{"key":"323_CR28","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/j.aml.2015.05.006","volume":"49","author":"J-H Zhang","year":"2015","unstructured":"Zhang, J.-H., Dai, H.: A new splitting preconditioner for the iterative solution of complex symmetric indefinite linear systems. Appl. Math. Lett. 49, 100\u2013106 (2015)","journal-title":"Appl. Math. Lett."},{"key":"323_CR29","doi-asserted-by":"publisher","unstructured":"Zheng, Q.-Q, Ma, C.-F.: Accelerated PMHSS iteration methods for complex symmetric linear systems. Numer. Algor. doi:\n                        10.1007\/s11075-016-0105-z","DOI":"10.1007\/s11075-016-0105-z"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-017-0323-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-017-0323-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-017-0323-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,1,20]],"date-time":"2018-01-20T01:41:11Z","timestamp":1516412471000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-017-0323-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,4,3]]},"references-count":29,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,2]]}},"alternative-id":["323"],"URL":"https:\/\/doi.org\/10.1007\/s11075-017-0323-z","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,4,3]]}}}