{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T03:24:08Z","timestamp":1762917848708},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2018,2,7]],"date-time":"2018-02-07T00:00:00Z","timestamp":1517961600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2019,2]]},"DOI":"10.1007\/s11075-018-0487-1","type":"journal-article","created":{"date-parts":[[2018,2,7]],"date-time":"2018-02-07T03:15:52Z","timestamp":1517973352000},"page":"337-354","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Efficient parameterized rotated shift-splitting preconditioner for a class of complex symmetric linear systems"],"prefix":"10.1007","volume":"80","author":[{"given":"Cheng-Liang","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chang-Feng","family":"Ma","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,2,7]]},"reference":[{"key":"487_CR1","doi-asserted-by":"publisher","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":"487_CR2","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1088\/0266-5611\/15\/2\/022","volume":"15","author":"SR Arridge","year":"1999","unstructured":"Arridge, S.R.: Optical tomography in medical imaging. Inverse Prob. 15, 41\u201393 (1999)","journal-title":"Inverse Prob."},{"key":"487_CR3","first-page":"49","volume":"18","author":"D Bertaccini","year":"2004","unstructured":"Bertaccini, D.: Efficient solvers for sequences of complex symmetric linear systems. Electron. Trans. Numer. Anal. 18, 49\u201364 (2004)","journal-title":"Electron. Trans. Numer. Anal."},{"key":"487_CR4","first-page":"49","volume":"18","author":"D Bertaccini","year":"2004","unstructured":"Bertaccini, D.: Efficient preconditioning for sequences of parametric complex symmetric linear systems. Electron. Tran. Numer. Anal. 18, 49\u201364 (2004)","journal-title":"Electron. Tran. Numer. Anal."},{"key":"487_CR5","doi-asserted-by":"publisher","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":"IMA J. Numer. Anal."},{"key":"487_CR6","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1007\/s00211-006-0679-9","volume":"103","author":"M Benzi","year":"2006","unstructured":"Benzi, M., Simoncini, V.: On the eigenvalues of a class of saddle point matrices. Numer. Math. 103, 173\u2013196 (2006)","journal-title":"Numer. Math."},{"key":"487_CR7","doi-asserted-by":"publisher","first-page":"791","DOI":"10.1090\/S0025-5718-05-01801-6","volume":"75","author":"Z-Z Bai","year":"2006","unstructured":"Bai, Z.-Z.: Structured preconditioners for nonsingular matrices of block two-by-two structures. Math. Comput. 75, 791\u2013815 (2006)","journal-title":"Math. Comput."},{"key":"487_CR8","doi-asserted-by":"publisher","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":"487_CR9","doi-asserted-by":"publisher","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. Algorithms 56, 297\u2013317 (2011)","journal-title":"Numer. Algorithms"},{"key":"487_CR10","doi-asserted-by":"publisher","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 applications to distributed control problems. IMA J. Numer. Anal. 33, 343\u2013369 (2013)","journal-title":"IMA J. Numer. Anal."},{"key":"487_CR11","doi-asserted-by":"publisher","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":"487_CR12","doi-asserted-by":"publisher","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":"487_CR13","doi-asserted-by":"publisher","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":"487_CR14","doi-asserted-by":"publisher","first-page":"655","DOI":"10.1007\/s11075-013-9696-9","volume":"64","author":"Z-Z Bai","year":"2013","unstructured":"Bai, Z.-Z., Chen, F., Wang, Z.-Q.: Additive block diagonal preconditioning for block two-by-two linear systems of skew-Hamiltonian coefficient matrices. Numer. Algorithms 64, 655\u2013675 (2013)","journal-title":"Numer. Algorithms"},{"key":"487_CR15","doi-asserted-by":"publisher","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":"487_CR16","doi-asserted-by":"publisher","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":"487_CR17","first-page":"539","volume":"24","author":"Z-Z Bai","year":"2006","unstructured":"Bai, Z.-Z., Yin, J.-F., Su, Y.-F.: A shift-splitting preconditioner for non-Hermitian positive definite matrices. J. Comput. Math. 24, 539\u2013552 (2006)","journal-title":"J. Comput. Math."},{"key":"487_CR18","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/S0096-3003(99)00027-2","volume":"109","author":"Z-Z Bai","year":"2000","unstructured":"Bai, Z.-Z.: Sharp error bounds of some Krylov subspace methods for non-Hermitian linear systems. Appl. Math. Comput. 109, 273\u2013285 (2000)","journal-title":"Appl. Math. Comput."},{"key":"487_CR19","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/j.cam.2015.01.025","volume":"283","author":"Z-Z Bai","year":"2015","unstructured":"Bai, Z.-Z.: Motivations and realizations of Krylov subspace methods for large sparse linear systems. J. Comput. Appl. Math. 283, 71\u201378 (2015)","journal-title":"J. Comput. Appl. Math."},{"key":"487_CR20","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/j.aml.2014.12.001","volume":"43","author":"C-R Chen","year":"2015","unstructured":"Chen, C.-R., Ma, C.-F.: A generalized shift-splitting preconditioner for saddle point problems. Appl. Math. Lett. 43, 49\u201355 (2015)","journal-title":"Appl. Math. Lett."},{"key":"487_CR21","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1016\/j.amc.2015.08.020","volume":"269","author":"C-R Chen","year":"2015","unstructured":"Chen, C.-R., Ma, C.-F.: A generalized shift-splitting preconditioner for singular saddle point problems. Appl. Math. Comput. 269, 947\u2013955 (2015)","journal-title":"Appl. Math. Comput."},{"key":"487_CR22","doi-asserted-by":"publisher","first-page":"2462","DOI":"10.1016\/j.camwa.2016.09.005","volume":"72","author":"C-R Chen","year":"2016","unstructured":"Chen, C.-R., Ma, C.-F.: AOR-Uzawa iterative method for a class of complex symmetric linear system of equations. Comput. Math. Appl. 72, 2462\u20132472 (2016)","journal-title":"Comput. Math. Appl."},{"key":"487_CR23","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1016\/j.cam.2014.05.017","volume":"272","author":"Y Cao","year":"2014","unstructured":"Cao, Y., Du, J., Niu, Q.: Shift-splitting preconditioners for saddle point problems. J. Comput. Appl. Math. 272, 239\u2013250 (2014)","journal-title":"J. Comput. Appl. Math."},{"key":"487_CR24","doi-asserted-by":"publisher","first-page":"1503","DOI":"10.1016\/j.camwa.2016.02.027","volume":"71","author":"Y Cao","year":"2016","unstructured":"Cao, Y., Miao, S.-X.: On semi-convergence of the generalized shift-splitting iteration method for singular nonsymmetric saddle point problems. Comput. Math. Appl. 71, 1503\u20131511 (2016)","journal-title":"Comput. Math. Appl."},{"key":"487_CR25","doi-asserted-by":"publisher","first-page":"1719","DOI":"10.1016\/S0045-7825(00)00187-0","volume":"190","author":"A Feriani","year":"2000","unstructured":"Feriani, A., Perotti, F., Simoncini, V.: Iterative system solvers for the frequency analysis of linear mechanical systems. Comput. Methods Appl. Mech. Eng. 190, 1719\u20131739 (2000)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"487_CR26","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1007\/978-3-642-58333-9_6","volume":"15","author":"A Frommer","year":"2000","unstructured":"Frommer, A., Lippert, T., Medeke, B., Schilling, K.: Numerical challenges in lattice quantum chromodynamics. Lect. Notes Comput. Sci. Eng. 15, 66\u201383 (2000)","journal-title":"Lect. Notes Comput. Sci. Eng."},{"key":"487_CR27","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1137\/0913023","volume":"13","author":"RW Freund","year":"1992","unstructured":"Freund, R.W.: Conjugate gradient-type methods for linear systems with complex symmetric coefficient matrices. SIAM J. Sci. Stat. Comput. 13, 425\u2013448 (1992)","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"487_CR28","doi-asserted-by":"publisher","first-page":"761","DOI":"10.1002\/nla.1987","volume":"22","author":"D Hezari","year":"2015","unstructured":"Hezari, D., Edalatpour, V., Salkuyeh, D.K.: Preconditioned GSOR iterative method for a class of complex symmetric system of linear equations. Numer. Linear Algebra Appl. 22, 761\u2013776 (2015)","journal-title":"Numer. Linear Algebra Appl."},{"key":"487_CR29","doi-asserted-by":"publisher","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":"487_CR30","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.amc.2017.01.014","volume":"302","author":"S-T Ling","year":"2017","unstructured":"Ling, S.-T., Liu, Q.-B.: New local generalized shift-splitting preconditioners for saddle point problems. Appl. Math. Comput. 302, 58\u201367 (2017)","journal-title":"Appl. Math. Comput."},{"key":"487_CR31","doi-asserted-by":"publisher","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. Algorithms 66, 555\u2013568 (2014)","journal-title":"Numer. Algorithms"},{"key":"487_CR32","doi-asserted-by":"publisher","first-page":"802","DOI":"10.1080\/00207160.2014.912753","volume":"92","author":"DK Salkuyeh","year":"2015","unstructured":"Salkuyeh, D.K., Hezari, D., Edalatpour, V.: Generalized successive overrelaxation iterative method for a class of complex symmetric linear system of equations. Int. J. Comput. Math. 92, 802\u2013815 (2015)","journal-title":"Int. J. Comput. Math."},{"key":"487_CR33","doi-asserted-by":"publisher","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":"487_CR34","doi-asserted-by":"crossref","first-page":"825","DOI":"10.1016\/j.amc.2014.06.040","volume":"243","author":"H-Y Yan","year":"2014","unstructured":"Yan, H.-Y., Huang, Y.-M.: Splitting-based block preconditioning methods for block two-by-two matrices of real square blocks. Appl. Math. Comput. 243, 825\u2013837 (2014)","journal-title":"Appl. Math. Comput."},{"key":"487_CR35","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-1099-7","volume-title":"Matrix Theory","author":"F-Z Zhang","year":"2011","unstructured":"Zhang, F.-Z.: Matrix Theory. Springer, New York (2011)"},{"key":"487_CR36","doi-asserted-by":"publisher","first-page":"2124","DOI":"10.1016\/j.camwa.2016.04.002","volume":"71","author":"M-L Zeng","year":"2016","unstructured":"Zeng, M.-L., Ma, C.-F.: A parameterized SHSS iteration method for a class of complex symmetric system of linear equations. Comput. Math. Appl. 71, 2124\u20132131 (2016)","journal-title":"Comput. Math. Appl."},{"key":"487_CR37","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1016\/j.aml.2016.04.008","volume":"60","author":"J-H Zhang","year":"2016","unstructured":"Zhang, J.-H., Dai, H.: Inexact splitting-based block preconditioners for block two-by-two linear systems. Appl. Math. Lett. 60, 89\u201395 (2016)","journal-title":"Appl. Math. Lett."},{"key":"487_CR38","doi-asserted-by":"publisher","first-page":"2946","DOI":"10.1016\/j.camwa.2015.10.011","volume":"70","author":"M-L Zeng","year":"2015","unstructured":"Zeng, M.-L., Zhang, G.-F.: Parameterized rotated block preconditioning techniques for block two-by-two systems with application to complex linear systems. Comput. Math. Appl. 70, 2946\u20132957 (2015)","journal-title":"Comput. Math. Appl."},{"key":"487_CR39","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1016\/j.aml.2016.11.009","volume":"66","author":"Q-Q Zheng","year":"2017","unstructured":"Zheng, Q.-Q., Lu, L.-Z.: A shift-splitting preconditioner for a class of block two-by-two linear systems. Appl. Math. Lett. 66, 54\u201360 (2017)","journal-title":"Appl. Math. Lett."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-018-0487-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-018-0487-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-018-0487-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,27]],"date-time":"2020-10-27T19:40:29Z","timestamp":1603827629000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-018-0487-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2,7]]},"references-count":39,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,2]]}},"alternative-id":["487"],"URL":"https:\/\/doi.org\/10.1007\/s11075-018-0487-1","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,2,7]]},"assertion":[{"value":"3 September 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 January 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 February 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}