{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T11:14:24Z","timestamp":1760267664167},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2019,4,26]],"date-time":"2019-04-26T00:00:00Z","timestamp":1556236800000},"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":["Comp. Appl. Math."],"published-print":{"date-parts":[[2019,6]]},"DOI":"10.1007\/s40314-019-0854-0","type":"journal-article","created":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T04:09:13Z","timestamp":1556338153000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Generalized fast shift-splitting preconditioner for nonsymmetric saddle-point problems"],"prefix":"10.1007","volume":"38","author":[{"given":"Jian-Hua","family":"Zhang","sequence":"first","affiliation":[]},{"given":"Xiao-Ping","family":"Chen","sequence":"additional","affiliation":[]},{"given":"Jing","family":"Zhao","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,4,26]]},"reference":[{"key":"854_CR1","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1002\/nla.1947","volume":"22","author":"O Axelsson","year":"2015","unstructured":"Axelsson O (2015) Unified analysis of preconditioning methods for saddle point matrices. Numer Linear Algebra Appl 22:233\u2013253","journal-title":"Numer Linear Algebra Appl"},{"key":"854_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1093\/imanum\/drl017","volume":"27","author":"Z-Z Bai","year":"2007","unstructured":"Bai Z-Z, Golub GH (2007) Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems. IMA J Numer Anal 27:1\u201323","journal-title":"IMA J Numer Anal"},{"key":"854_CR3","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 GH, Pan J-Y (2004) Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems. Numer Math 98:1\u201332","journal-title":"Numer Math"},{"key":"854_CR4","doi-asserted-by":"publisher","first-page":"603","DOI":"10.1137\/S0895479801395458","volume":"24","author":"Z-Z Bai","year":"2003","unstructured":"Bai Z-Z, Golub GH, Ng MK (2003) Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems. SIAM J Matrix Anal Appl 24:603\u2013626","journal-title":"SIAM J Matrix Anal Appl"},{"key":"854_CR5","first-page":"539","volume":"24","author":"Z-Z Bai","year":"2006","unstructured":"Bai Z-Z, Yin J-F, Su Y-F (2006) A shift-splitting preconditioner for non-Hermitian positive definite matrices. J Comput Math 24:539\u2013552","journal-title":"J Comput Math"},{"key":"854_CR6","doi-asserted-by":"publisher","first-page":"1710","DOI":"10.1137\/040604091","volume":"26","author":"Z-Z Bai","year":"2005","unstructured":"Bai Z-Z, Ng MK (2005) On inexact preconditioners for nonsymmetric matrices. SIAM J Sci Comput 26:1710\u20131724","journal-title":"SIAM J Sci Comput"},{"key":"854_CR7","doi-asserted-by":"publisher","first-page":"2900C","DOI":"10.1016\/j.laa.2008.01.018","volume":"428","author":"Z-Z Bai","year":"2008","unstructured":"Bai Z-Z, Wang Z-Q (2008) On parameterized inexact Uzawa methods for generalized saddle point problems. Linear Algebra Appl 428:2900C\u20132932","journal-title":"Linear Algebra Appl"},{"key":"854_CR8","doi-asserted-by":"publisher","first-page":"410","DOI":"10.1137\/080720243","volume":"31","author":"Z-Z Bai","year":"2009","unstructured":"Bai Z-Z, Ng MK, Wang Z-Q (2009) Constraint preconditioners for symmetric indefinite matrices. SIAM J Matrix Anal Appl 31:410\u2013433","journal-title":"SIAM J Matrix Anal Appl"},{"key":"854_CR9","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1137\/S0895479802417106","volume":"26","author":"M Benzi","year":"2004","unstructured":"Benzi M, Golub GH (2004) A preconditioner for generalized saddle point problems. SIAM J Matrix Anal Appl 26:20\u201341","journal-title":"SIAM J Matrix Anal Appl"},{"key":"854_CR10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1017\/S0962492904000212","volume":"14","author":"M Benzi","year":"2005","unstructured":"Benzi M, Golub GH, Liesen J (2005) Numerical solution of saddle point problems. Acta Numer 14:1\u2013137","journal-title":"Acta Numer"},{"key":"854_CR11","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 RJ (1994) Nonnegative matrices in the mathematical sciences. SIAM, Philadelphia"},{"key":"854_CR12","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 (2014) Shift-splitting preconditioners for saddle point problems. J Comput Appl Math 272:239\u2013250","journal-title":"J Comput Appl Math"},{"key":"854_CR13","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1016\/j.aml.2015.04.001","volume":"49","author":"Y Cao","year":"2015","unstructured":"Cao Y, Li S, Yao L-Q (2015) A class of generalized shift-splitting preconditioners for nonsymmetric saddle point problems. Appl Math Lett 49:20\u201327","journal-title":"Appl Math Lett"},{"key":"854_CR14","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 (2016) On semi-convergence of the generalized shift-splitting iteration method for singular nonsymmetric saddle point problems. Comput Math Appl 71:1503\u20131511","journal-title":"Comput Math Appl"},{"key":"854_CR15","doi-asserted-by":"publisher","first-page":"859","DOI":"10.1016\/j.camwa.2017.05.031","volume":"74","author":"Y Cao","year":"2017","unstructured":"Cao Y, Miao S-X, Ren Z-R (2017) On preconditioned generalized shift-splitting iteration methods for saddle point problems. Comput Math Appl 74:859\u2013872","journal-title":"Comput Math Appl"},{"key":"854_CR16","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 (2015) A generalized shift-splitting preconditioner for saddle point problems. Appl Math Lett 43:49\u201355","journal-title":"Appl Math Lett"},{"key":"854_CR17","doi-asserted-by":"publisher","first-page":"172","DOI":"10.4208\/eajam.170616.311216a","volume":"7","author":"Q-Y Dou","year":"2017","unstructured":"Dou Q-Y, Yin J-F, Liao Z-Y (2017) A fast shift-splitting iteration method for nonsymmetric saddle point problems. East Asian J Appl Math 7:172\u2013191","journal-title":"East Asian J Appl Math"},{"key":"854_CR18","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1016\/S0168-9274(02)00118-6","volume":"43","author":"HC Elman","year":"2002","unstructured":"Elman HC (2002) Preconditioners for saddle point problems arising in computational fluid dynamics. Appl Numer Math 43:75\u201389","journal-title":"Appl Numer Math"},{"key":"854_CR19","doi-asserted-by":"publisher","first-page":"665","DOI":"10.1007\/s002110100300","volume":"90","author":"HC Elman","year":"2002","unstructured":"Elman HC, Silvester DJ, Wathen AJ (2002) Performance and analysis of saddle point preconditioners for the discrete steady-state Navier\u2013Stokes equations. Numer Math 90:665\u2013688","journal-title":"Numer Math"},{"key":"854_CR20","first-page":"95","volume":"299","author":"Z-G Huang","year":"2017","unstructured":"Huang Z-G, Wang L-G, Xu Z, Cui J-J (2017) The generalized modified shift-splitting preconditioners for nonsymmetric saddle point problems. Appl Math Comput 299:95\u2013118","journal-title":"Appl Math Comput"},{"key":"854_CR21","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1016\/j.camwa.2017.09.016","volume":"75","author":"Z-G Huang","year":"2018","unstructured":"Huang Z-G, Wang L-G, Xu Z, Cui J-J (2018) Parameterized generalized shift-splitting preconditioners for nonsymmetric saddle point problems. Comput Math Appl 75:349\u2013373","journal-title":"Comput Math Appl"},{"key":"854_CR22","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1016\/j.cam.2016.11.032","volume":"317","author":"Z-H Huang","year":"2017","unstructured":"Huang Z-H, Su H (2017) A modified shift-splitting method for nonsymmetric saddle point problems. J Comput Appl Math 317:535\u2013546","journal-title":"J Comput Appl Math"},{"key":"854_CR23","doi-asserted-by":"publisher","first-page":"973","DOI":"10.1016\/j.cam.2009.05.012","volume":"231","author":"M-Q Jiang","year":"2009","unstructured":"Jiang M-Q, Cao Y (2009) On local Hermitian and skew-Hermitian splitting iteration methods for generalized saddle point problems. J Comput Appl Math 231:973\u2013982","journal-title":"J Comput Appl Math"},{"key":"854_CR24","first-page":"1777","volume":"216","author":"M-Q Jiang","year":"2010","unstructured":"Jiang M-Q, Cao Y, Yao L-Q (2010) On parameterized block triangular preconditioners for generalized saddle point problems. Appl Math Comput 216:1777\u20131789","journal-title":"Appl Math Comput"},{"key":"854_CR25","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1093\/imamat\/8.3.397","volume":"8","author":"JJH Miller","year":"1971","unstructured":"Miller JJH (1971) On the location of zeros of certain classes of polynomials with applications to numerical analysis. J Inst Math Appl 8:397\u2013406","journal-title":"J Inst Math Appl"},{"key":"854_CR26","doi-asserted-by":"publisher","DOI":"10.1007\/b98874","volume-title":"Numerical optimization","author":"J Nocedal","year":"1999","unstructured":"Nocedal J, Wright S (1999) Numerical optimization. Springer, New York"},{"key":"854_CR27","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1016\/j.cam.2016.08.031","volume":"311","author":"Z-R Ren","year":"2017","unstructured":"Ren Z-R, Cao Y, Niu Q (2017) Spectral analysis of the generalized shift-splitting preconditioned saddle point problem. J Comput Appl Math 311:539\u2013550","journal-title":"J Comput Appl Math"},{"key":"854_CR28","doi-asserted-by":"publisher","first-page":"856","DOI":"10.1137\/0907058","volume":"7","author":"Y Saad","year":"1986","unstructured":"Saad Y, Schultz MH (1986) GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7:856\u2013869","journal-title":"SIAM J Sci Stat Comput"},{"key":"854_CR29","doi-asserted-by":"publisher","first-page":"2940","DOI":"10.1016\/j.camwa.2017.07.029","volume":"74","author":"DK Salkuyeh","year":"2017","unstructured":"Salkuyeh DK, Rahimian M (2017) A modification of the generalized shift-splitting method for singular saddle point problems. Comput Math Appl 74:2940\u20132949","journal-title":"Comput Math Appl"},{"key":"854_CR30","doi-asserted-by":"publisher","first-page":"571","DOI":"10.1016\/0377-0427(95)00167-0","volume":"66","author":"JY Yuan","year":"1996","unstructured":"Yuan JY (1996) Numerical methods for generalized least squares problems. J Comput Appl Math 66:571\u2013584","journal-title":"J Comput Appl Math"},{"key":"854_CR31","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1016\/0377-0427(95)00239-1","volume":"71","author":"JY Yuan","year":"1996","unstructured":"Yuan JY, Iusem AN (1996) Preconditioned conjugate gradient method for generalized least squares problems. J Comput Appl Math 71:287\u2013297","journal-title":"J Comput Appl Math"},{"key":"854_CR32","doi-asserted-by":"publisher","first-page":"808","DOI":"10.1016\/j.laa.2009.03.033","volume":"431","author":"B Zheng","year":"2009","unstructured":"Zheng B, Bai Z-Z, Yang X (2009) On semi-convergence of parameterized Uzawa methods for singular saddle point problems. Linear Algebra Appl 431:808\u2013817","journal-title":"Linear Algebra Appl"},{"key":"854_CR33","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.cam.2016.09.008","volume":"313","author":"Q-Q Zheng","year":"2017","unstructured":"Zheng Q-Q, Lu L-Z (2017) Extended shift-splitting preconditioners for saddle point problems. J Comput Appl Math 313:70\u201381","journal-title":"J Comput Appl Math"},{"key":"854_CR34","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1016\/j.aml.2016.03.011","volume":"59","author":"S-W Zhou","year":"2016","unstructured":"Zhou S-W, Yang A-L, Dou Y, Wu Y-J (2016) The modified shift-splitting preconditioners for nonsymmetric saddle point problems. Appl Math Lett 59:109\u2013114","journal-title":"Appl Math Lett"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-019-0854-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s40314-019-0854-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-019-0854-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,24]],"date-time":"2020-04-24T23:08:48Z","timestamp":1587769728000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s40314-019-0854-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,26]]},"references-count":34,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,6]]}},"alternative-id":["854"],"URL":"https:\/\/doi.org\/10.1007\/s40314-019-0854-0","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,4,26]]},"assertion":[{"value":"18 May 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 December 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 December 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 April 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"92"}}