{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T11:07:22Z","timestamp":1760267242866},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2013,8,18]],"date-time":"2013-08-18T00:00:00Z","timestamp":1376784000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2014,8]]},"DOI":"10.1007\/s11075-013-9755-2","type":"journal-article","created":{"date-parts":[[2013,8,17]],"date-time":"2013-08-17T02:08:01Z","timestamp":1376705281000},"page":"705-719","source":"Crossref","is-referenced-by-count":8,"title":["The semi-convergence properties of MHSS method for a class of complex nonsymmetric singular linear systems"],"prefix":"10.1007","volume":"66","author":[{"given":"Ai-Li","family":"Yang","sequence":"first","affiliation":[]},{"given":"Yu-Jiang","family":"Wu","sequence":"additional","affiliation":[]},{"given":"Zhen-Jian","family":"Xu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2013,8,18]]},"reference":[{"key":"9755_CR1","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1103\/RevModPhys.74.99","volume":"74","author":"IS Aranson","year":"2002","unstructured":"Aranson, I.S., Kramer, L.: The world of the complex Ginzburg-Landau equation. Rev. Mod. Phys. 74, 99\u2013143 (2002)","journal-title":"Rev. Mod. Phys."},{"key":"9755_CR2","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/s00607-010-0101-4","volume":"89","author":"Z-Z Bai","year":"2010","unstructured":"Bai, Z.-Z.: On semi-convergence of Hermitian and skew-Hermitian splitting methods for singular linear systems. Computing 89, 171\u2013197 (2010)","journal-title":"Computing"},{"key":"9755_CR3","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":"9755_CR4","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":"IMA J. Numer. Anal."},{"key":"9755_CR5","doi-asserted-by":"crossref","first-page":"844","DOI":"10.1137\/S1064827503428114","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":"SIAM J. Sci. Comput."},{"key":"9755_CR6","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1137\/S0895479801395458","volume":"24","author":"Z-Z Bai","year":"2002","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 (2002)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9755_CR7","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/j.laa.2007.02.018","volume":"428","author":"Z-Z Bai","year":"2008","unstructured":"Bai, Z.-Z., Golub, G.H., Ng, M.K.: On inexact Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems. Linear Algebra Appl. 428, 413\u2013440 (2008)","journal-title":"Linear Algebra Appl."},{"key":"9755_CR8","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":"9755_CR9","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/S0168-9274(03)00057-6","volume":"47","author":"Z-Z Bai","year":"2003","unstructured":"Bai, Z.-Z., Wang, L., Yuan, J.-Y.: Weak-convergence theory of quasi-nonnegative splittings for singular matrices. Appl. Numer. Math. 47, 75\u201389 (2003)","journal-title":"Appl. Numer. Math."},{"key":"9755_CR10","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":"IMA J. Numer. Anal."},{"key":"9755_CR11","doi-asserted-by":"crossref","first-page":"881","DOI":"10.1023\/B:BITN.0000014548.26616.65","volume":"43","author":"M Benzi","year":"2003","unstructured":"Benzi, M., Gander, M., Golub, G.: Optimization of the Hermitian and skew-Hermitian splitting iteration for saddle-point problems. BIT Numer. Math. 43, 881\u2013900 (2003)","journal-title":"BIT Numer. Math."},{"key":"9755_CR12","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1137\/S0895479802417106","volume":"26","author":"M Benzi","year":"2005","unstructured":"Benzi, M., Golub, G.H.: A preconditioner for generalized saddle point problems. SIAM J. Matrix Anal. Appl. 26, 20\u201341 (2005)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9755_CR13","doi-asserted-by":"crossref","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. SIAM, Philadephia (1994)"},{"key":"9755_CR14","first-page":"49","volume":"18","author":"D Bertaccini","year":"2004","unstructured":"Bertaccini, D.: Efficient preconditioning for sequences of parametric complex symmetric linear systems. Electr. Trans. Numer. Anal. 18, 49\u201364 (2004)","journal-title":"Electr. Trans. Numer. Anal."},{"key":"9755_CR15","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1007\/s00211-004-0574-1","volume":"99","author":"D Bertaccini","year":"2005","unstructured":"Bertaccini, D., Golub, G.H., Capizzano, S.S., Possio, C.T.: Preconditioned HSS methods for the solution of non-Hermitian positive definite linear systems and applications to the discrete convection-diffusion equation. Numer. Math. 99, 441\u2013484 (2005)","journal-title":"Numer. Math."},{"key":"9755_CR16","doi-asserted-by":"crossref","unstructured":"Chen, F., Liu, Q.-Q.: On semi-convergence of modified HSS iteration methods. Numer. Algor. (2012). doi: 10.1007\/s11075-012-9676-5","DOI":"10.1007\/s11075-012-9676-5"},{"key":"9755_CR17","doi-asserted-by":"crossref","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":"9755_CR18","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1561\/0100000006","volume":"2","author":"R Gray","year":"2006","unstructured":"Gray, R.: Toeplitz and circulant matrices: a review. Found. Trends Commun. Inform. Theory 2, 155\u2013239 (2006)","journal-title":"Found. Trends Commun. Inform. Theory"},{"key":"9755_CR19","doi-asserted-by":"crossref","first-page":"441","DOI":"10.4208\/jcm.1103-m3422","volume":"29","author":"G-D Gu","year":"2011","unstructured":"Gu, G.-D.: HSS method with a complex parameter for the solution of complex linear system. J. Comput. Math. 29, 441\u2013457 (2011)","journal-title":"J. Comput. Math."},{"key":"9755_CR20","doi-asserted-by":"crossref","first-page":"10, 122","DOI":"10.1016\/j.amc.2012.03.088","volume":"218","author":"X-X Guo","year":"2012","unstructured":"Guo, X.-X., Wang, S.: Modified HSS iteration methods for a class of non-Hermitian positive-definite linear systems. Appl. Math. Comput. 218, 10, 122\u201310, 128 (2012)","journal-title":"Appl. Math. Comput."},{"key":"9755_CR21","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970944","volume-title":"Iterative Methods for Linear and Nonlinear Equations","author":"CT Kelley","year":"1995","unstructured":"Kelley, C.T.: Iterative Methods for Linear and Nonlinear Equations. SIAM, Philadelphia (1995)"},{"key":"9755_CR22","volume-title":"Chemical Oscillations, Waves, and Turbulence","author":"Y Kuramoto","year":"2003","unstructured":"Kuramoto, Y.: Chemical Oscillations, Waves, and Turbulence. Dover Publications, Inc., Mineola (2003)"},{"key":"9755_CR23","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1002\/nla.528","volume":"14","author":"L Li","year":"2007","unstructured":"Li, L., Huang, T.-Z., Liu, X.-P.: Modified Hermitian and skew-Hermitian splitting methods for non-Hermitian positive-definite linear systems. Numer. Linear Algebra Appl. 14, 217\u2013235 (2007)","journal-title":"Numer. Linear Algebra Appl."},{"key":"9755_CR24","doi-asserted-by":"crossref","first-page":"2338","DOI":"10.1016\/j.cam.2011.11.020","volume":"236","author":"W Li","year":"2012","unstructured":"Li, W., Liu, Y.-P., Peng, X.-F.: The generalized HSS method for solving singular linear systems. J. Comput. Appl. Math. 236, 2338\u20132353 (2012)","journal-title":"J. Comput. Appl. Math."},{"key":"9755_CR25","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1002\/1099-1506(200010\/12)7:7\/8<715::AID-NLA220>3.0.CO;2-R","volume":"7","author":"B Poirier","year":"2000","unstructured":"Poirier, B.: Efficient preconditioning scheme for block partitioned matrices with structured sparsity. Numer. Linear Algebra Appl. 7, 715\u2013726 (2000)","journal-title":"Numer. Linear Algebra Appl."},{"key":"9755_CR26","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":"9755_CR27","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/s002110050479","volume":"85","author":"Y Song","year":"2000","unstructured":"Song, Y.: Semiconvergence of nonnegative splittings for singular matrices. Numer. Math. 85, 109\u2013127 (2000)","journal-title":"Numer. Math."},{"key":"9755_CR28","volume-title":"The nonlinear Schr\u00f6dinger equation, self-focusing and wave collapse. Applied Mathematical Sciences, vol. 39","author":"C Sulem","year":"1999","unstructured":"Sulem, C., Sulem, P.L.: The nonlinear Schr\u00f6dinger equation, self-focusing and wave collapse. Applied Mathematical Sciences, vol. 39. Springer, New York (1999)"},{"key":"9755_CR29","doi-asserted-by":"crossref","first-page":"1715","DOI":"10.1016\/j.amc.2009.12.032","volume":"216","author":"A-L Yang","year":"2010","unstructured":"Yang, A.-L., An, J., Wu, Y.-J.: A generalized preconditioned HSS method for non-Hermitian positive definite linear systems. Appl. Math. Comput. 216, 1715\u20131722 (2010)","journal-title":"Appl. Math. Comput."},{"key":"9755_CR30","doi-asserted-by":"crossref","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.: On semi-convergence of parameterized Uzawa methods for singular saddle point problems. Linear Algebra Appl. 431, 808\u2013817 (2009)","journal-title":"Linear Algebra Appl."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-013-9755-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-013-9755-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-013-9755-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T01:08:22Z","timestamp":1559351302000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-013-9755-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,8,18]]},"references-count":30,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2014,8]]}},"alternative-id":["9755"],"URL":"https:\/\/doi.org\/10.1007\/s11075-013-9755-2","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,8,18]]}}}