{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T11:10:26Z","timestamp":1760267426987},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2016,8,25]],"date-time":"2016-08-25T00:00:00Z","timestamp":1472083200000},"content-version":"unspecified","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":[[2017,5]]},"DOI":"10.1007\/s11075-016-0196-6","type":"journal-article","created":{"date-parts":[[2016,8,25]],"date-time":"2016-08-25T00:43:51Z","timestamp":1472085831000},"page":"55-80","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Multi-step modified Newton-HSS methods for systems of nonlinear equations with positive definite Jacobian matrices"],"prefix":"10.1007","volume":"75","author":[{"given":"Yang","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xue-Ping","family":"Guo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,8,25]]},"reference":[{"key":"196_CR1","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1016\/j.apnum.2006.02.007","volume":"57","author":"H-B An","year":"2007","unstructured":"An, H.-B., Bai, Z.-Z.: A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations. Appl. Numer. Math. 57, 235\u2013252 (2007)","journal-title":"Appl. Numer. Math."},{"key":"196_CR2","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1016\/0045-7825(85)90094-5","volume":"50","author":"O Axelsson","year":"1985","unstructured":"Axelsson, O., Carey, C.F.: On the numerical solution of two-point singularly perturbed boundary value problems. Appl. Mech. Engrg. 50, 217\u2013229 (1985)","journal-title":"Appl. Mech. Engrg."},{"key":"196_CR3","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1007\/BF02684384","volume":"61","author":"O Axelsson","year":"1998","unstructured":"Axelsson, O., Nikolova, M.: Avoiding slave points in an adaptive refinement procedure for convection-diffusion problems in 2D. Computing 61, 331\u2013357 (1998)","journal-title":"Computing"},{"key":"196_CR4","doi-asserted-by":"publisher","first-page":"801","DOI":"10.14492\/hokmj\/1272848034","volume":"36","author":"Z-Z Bai","year":"2007","unstructured":"Bai, Z.-Z.: Splitting iteration methods for non-Hermitian positive definite systems of linear equations. Hokkaido Math. J. 36, 801\u2013814 (2007)","journal-title":"Hokkaido Math. J."},{"key":"196_CR5","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":"196_CR6","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, 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":"196_CR7","doi-asserted-by":"crossref","first-page":"235","DOI":"10.4208\/jcm.2009.10-m2836","volume":"28","author":"Z-Z Bai","year":"2010","unstructured":"Bai, Z.-Z., Guo, X.-P.: On Newton-HSS methods for systems of nonlinear equations with positive-definite Jacobian matrices. J. Comput. Math. 28, 235\u2013260 (2010)","journal-title":"J. Comput. Math."},{"key":"196_CR8","doi-asserted-by":"publisher","first-page":"881","DOI":"10.1023\/B:BITN.0000014548.26616.65","volume":"43","author":"M Benzi","year":"2003","unstructured":"Benzi, M., Gander, M.J., Golub, G.H.: Optimization of the Hermitian and skew-Hermitian splitting iteration for saddle-point problems. BIT Numer. Math. 43, 881\u2013990 (2003)","journal-title":"BIT Numer. Math."},{"key":"196_CR9","doi-asserted-by":"publisher","first-page":"583","DOI":"10.1137\/050623644","volume":"28","author":"Z-Z Bai","year":"2006","unstructured":"Bai, Z.-Z., Golub, G.H., Li, C.-K.: Optimal parameter in Hermitian and skew-Hermitian splitting method for certain two-by-two block matrices. SIAM J. Sci. Comput. 28, 583\u2013603 (2006)","journal-title":"SIAM J. Sci. Comput."},{"key":"196_CR10","doi-asserted-by":"publisher","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":"196_CR11","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1090\/S0025-5718-06-01892-8","volume":"76","author":"Z-Z Bai","year":"2007","unstructured":"Bai, Z.-Z., Golub, G.H., Li, C.-K.: Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices. Math. Comp. 76, 287\u2013298 (2007)","journal-title":"Math. Comp."},{"key":"196_CR12","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":"196_CR13","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":"196_CR14","doi-asserted-by":"publisher","first-page":"450","DOI":"10.1137\/0911026","volume":"11","author":"PN Brown","year":"1990","unstructured":"Brown, P.N., Saad, Y.: Hybrid Krylov methods for nonlinear systems of equations. SIAM J. Sci. Stat. Comput. 11, 450\u2013481 (1990)","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"196_CR15","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1137\/0804017","volume":"4","author":"PN Brown","year":"1994","unstructured":"Brown, P.N., Saad, Y.: Convergence theory of nonlinear Newton-Krylov algorithms. SIAM J. Optim. 4, 297\u2013330 (1994)","journal-title":"SIAM J. Optim."},{"key":"196_CR16","doi-asserted-by":"crossref","first-page":"630","DOI":"10.1016\/j.amc.2006.08.080","volume":"187","author":"MT Darvishi","year":"2007","unstructured":"Darvishi, M.T., Barati, A.: A third-order Newton-type method to solve systems of nonlinear equations. Appl. Math. Comput. 187, 630\u2013635 (2007)","journal-title":"Appl. Math. Comput."},{"key":"196_CR17","doi-asserted-by":"publisher","first-page":"400","DOI":"10.1137\/0719025","volume":"19","author":"RS Dembo","year":"1982","unstructured":"Dembo, R.S., Eisenstat, S.C., Steihaug, T.: Inexact Newton methods. SIAM J. Numer. Anal. 19, 400\u2013408 (1982)","journal-title":"SIAM J. Numer. Anal."},{"key":"196_CR18","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1137\/0804022","volume":"4","author":"SC Eisenstat","year":"1994","unstructured":"Eisenstat, S.C., Walker, H.F.: Globally convergent inexact Newton methods. SIAM J. Optim. 4, 393\u2013422 (1994)","journal-title":"SIAM J. Optim."},{"key":"196_CR19","first-page":"231","volume":"25","author":"X-P Guo","year":"2007","unstructured":"Guo, X.-P.: On semilocal convergence of inexact Newton methods. J. Comput. Math. 25, 231\u2013242 (2007)","journal-title":"J. Comput. Math."},{"key":"196_CR20","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1002\/nla.713","volume":"18","author":"X-P Guo","year":"2011","unstructured":"Guo, X.-P., Duff, I.S.: Semilocal and global convergence of the Newton-HSS method for systems of nonlinear equations. Numer. Linear Algebra Appl. 18, 299\u2013315 (2011)","journal-title":"Numer. Linear Algebra Appl."},{"key":"196_CR21","doi-asserted-by":"publisher","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":"196_CR22","volume-title":"Functional Analysis","author":"LV Kantorovich","year":"1982","unstructured":"Kantorovich, L.V., Akilov, G.P.: Functional Analysis. Pergamon Press, Oxford (1982)"},{"key":"196_CR23","volume-title":"Iterative Solution of Nonlinear Equations in Several Variables","author":"JM Ortega","year":"1970","unstructured":"Ortega, J.M., Rheinboldt, W.C.: Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York (1970)"},{"key":"196_CR24","doi-asserted-by":"publisher","first-page":"659","DOI":"10.1007\/s11075-012-9684-5","volume":"64","author":"Q-B Wu","year":"2013","unstructured":"Wu, Q.-B., Chen, M.-H.: Convergence analysis of modified Newton-HSS method for solving systems of nonlinear equations. Numer. Algor. 64, 659\u2013683 (2013)","journal-title":"Numer. Algor."},{"key":"196_CR25","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970012","volume-title":"Methods of Solving Systems of Nonlinear Equations","author":"WC Rheinboldt","year":"1998","unstructured":"Rheinboldt, W.C.: Methods of Solving Systems of Nonlinear Equations, 2nd edn. SIAM, Philadelphia (1998)","edition":"2nd edn"},{"key":"196_CR26","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718003","volume-title":"Iterative Methods for Sparse Linear and Nonlinear Equations","author":"Y Saad","year":"2003","unstructured":"Saad, Y.: Iterative Methods for Sparse Linear and Nonlinear Equations, 2nd edn. SIAM, Philadelphia (2003)","edition":"2nd edn"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-016-0196-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-016-0196-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-016-0196-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-016-0196-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,25]],"date-time":"2020-09-25T13:59:10Z","timestamp":1601042350000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-016-0196-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,8,25]]},"references-count":26,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,5]]}},"alternative-id":["196"],"URL":"https:\/\/doi.org\/10.1007\/s11075-016-0196-6","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,8,25]]}}}