{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T11:26:28Z","timestamp":1751628388173},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2010,2,6]],"date-time":"2010-02-06T00:00:00Z","timestamp":1265414400000},"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":[[2010,12]]},"DOI":"10.1007\/s11075-010-9367-z","type":"journal-article","created":{"date-parts":[[2010,2,4]],"date-time":"2010-02-04T23:19:57Z","timestamp":1265325597000},"page":"481-502","source":"Crossref","is-referenced-by-count":26,"title":["Practical Quasi-Newton algorithms for singular nonlinear systems"],"prefix":"10.1007","volume":"55","author":[{"given":"Sandra","family":"Buhmiler","sequence":"first","affiliation":[]},{"given":"Nata\u0161a","family":"Kreji\u0107","sequence":"additional","affiliation":[]},{"given":"Zorana","family":"Lu\u017eanin","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2010,2,6]]},"reference":[{"key":"9367_CR1","doi-asserted-by":"crossref","first-page":"1199","DOI":"10.1137\/S1064827596297549","volume":"21","author":"A Bouaricha","year":"1999","unstructured":"Bouaricha, A., Schnabel, R.B.: Tensor methods for nonlinear least squares problems. SIAM J. Sci. Comput. 21, 1199\u20131221 (1999)","journal-title":"SIAM J. Sci. Comput."},{"key":"9367_CR2","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1090\/S0025-5718-1965-0198670-6","volume":"19","author":"G Broyden","year":"1965","unstructured":"Broyden, G.: A class of methods for solving nonlinear simultaneous equations. Math. Comput. 19, 577\u2013593 (1965)","journal-title":"Math. Comput."},{"key":"9367_CR3","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.cam.2006.11.007","volume":"211","author":"S Buhmiler","year":"2008","unstructured":"Buhmiler, S., Kreji\u0107, N.: A new smoothing quasi-Newton method for nonlinear complementarity problems. J. Comput. Appl. Math. 211, 141\u2013155 (2008)","journal-title":"J. Comput. Appl. Math."},{"key":"9367_CR4","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1137\/0717009","volume":"17","author":"DW Decker","year":"1980","unstructured":"Decker, D.W., Kelley, C.T.: Newton\u2019s method at singular point I. SIAM J. Numer. Anal. 17, 66\u201370 (1980)","journal-title":"SIAM J. Numer. Anal."},{"key":"9367_CR5","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/BF01395307","volume":"42","author":"DW Decker","year":"1983","unstructured":"Decker, D.W., Kelley, C.T.: Sublinear convergence of the chord method at singular point. Numer. Math. 42, 147\u2013154 (1983)","journal-title":"Numer. Math."},{"issue":"3","key":"9367_CR6","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1137\/0722034","volume":"22","author":"DW Decker","year":"1985","unstructured":"Decker, D.W., Kelley, C.T.: Broyden\u2019s method for a class of problems having singular Jacobian at the root. SIAM J. Numer. Anal. 22(3), 566\u2013573 (1985)","journal-title":"SIAM J. Numer. Anal."},{"key":"9367_CR7","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1007\/BF01585177","volume":"62","author":"D Feng","year":"1993","unstructured":"Feng, D., Frank, P.D., Schnabel, R.B.: Local convergence analysis of tensor methods for nonlinear equations. Math. Program. 62, 427\u2013459 (1993)","journal-title":"Math. Program."},{"key":"9367_CR8","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1137\/1027141","volume":"27","author":"A Griewank","year":"1985","unstructured":"Griewank, A.: On solving nonlinear equations with simple singularities or nearly singular solutions. SIAM Rev. 27, 537\u2013563 (1985)","journal-title":"SIAM Rev."},{"key":"9367_CR9","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1017\/S0334270000005208","volume":"28","author":"A Griewank","year":"1986","unstructured":"Griewank, A.: The \u201cglobal\u201d convergence of Broyden-like methods with a suitable line search. J. Aust. Math. Soc. Series B 28, 75\u201392 (1986)","journal-title":"J. Aust. Math. Soc. Series B"},{"key":"9367_CR10","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1137\/S1052623403432633","volume":"15","author":"R Hauser","year":"2005","unstructured":"Hauser, R., Nedi\u0107, J: The continuous Newton\u2013Raphson method can look ahead. SIAM J. Optim. 15, 915\u2013925 (2005)","journal-title":"SIAM J. Optim."},{"key":"9367_CR11","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1137\/040620631","volume":"18","author":"R Hauser","year":"2007","unstructured":"Hauser, R., Nedi\u0107, J.: On the relationship between the convergence rates of iterative and continuous processes. SIAM J. Optim. 18, 52\u201364 (2007)","journal-title":"SIAM J. Optim."},{"key":"9367_CR12","doi-asserted-by":"crossref","first-page":"2068","DOI":"10.1137\/S003614299224185X","volume":"33","author":"V Janovsky","year":"1996","unstructured":"Janovsky, V., Seigre, V.: Qualitative analysis of Newton\u2019s flow. SIAM J. Numer. Anal. 33, 2068\u20132097 (1996)","journal-title":"SIAM J. Numer. Anal."},{"key":"9367_CR13","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.1137\/0720070","volume":"20","author":"CT Kelley","year":"1983","unstructured":"Kelley, C.T., Suresh, R.: A new acceleration method for Newton\u2019s method at singular point. SIAM J. Numer. Anal. 20, 1001\u20131009 (1983)","journal-title":"SIAM J. Numer. Anal."},{"key":"9367_CR14","first-page":"609","volume":"47","author":"CT Kelley","year":"1986","unstructured":"Kelley, C.T.: A Shamanskii-like acceleration scheme for nonlinear equations at singular point. Math. Comput. 47, 609\u2013623 (1986)","journal-title":"Math. Comput."},{"key":"9367_CR15","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1080\/10556789308805545","volume":"2","author":"CT Kelley","year":"1993","unstructured":"Kelley, C.T., Xue, Z.Q.: Inexact Newton methods for singular problems. Optim. Methods Softw. 2, 249\u2013267 (1993)","journal-title":"Optim. Methods Softw."},{"key":"9367_CR16","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1007\/BF02193101","volume":"81","author":"L Luk\u0161an","year":"1994","unstructured":"Luk\u0161an,L.: Inexact Trust Region Method for Large Sparse Systems of Nonlinear Equations. J Opt. Theory Appl. 81, 569\u2013590 (1994)","journal-title":"J Opt. Theory Appl."},{"key":"9367_CR17","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1007\/BF02242278","volume":"3","author":"JM Mart\u00ednez","year":"1984","unstructured":"Mart\u00ednez, J.M.: A quasi-Newton method with modification of one column per iteration. Computing 3, 353\u2013362 (1984)","journal-title":"Computing"},{"key":"9367_CR18","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/S0377-0427(00)00434-9","volume":"124","author":"JM Mart\u00ednez","year":"2000","unstructured":"Mart\u00ednez, J.M.: Practical quasi-Newton methods for solving nonlinear systems. J. Comput. Appl. Math. 124, 97\u2013121 (2000)","journal-title":"J. Comput. Appl. Math."},{"key":"9367_CR19","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/S0377-0427(03)00451-5","volume":"158","author":"LF Mendon\u00e7a de","year":"2003","unstructured":"de Mendon\u00e7a, L.F., P\u00e9rez, R., Lopes, V.L.R.: Inverse q-columns updates methods for solving nonlinear system of equations. J. Comput. Appl. Math. 158, 317\u2013337 (2003)","journal-title":"J. Comput. Appl. Math."},{"key":"9367_CR20","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1080\/00029890.2007.11920431","volume":"114","author":"JW Neuberger","year":"2007","unstructured":"Neuberger, J.W.: The continuous Newton\u2019s method, inverse functions and Nash\u2013Moser. Am. Math. Mon. 114, 432\u2013437 (2007)","journal-title":"Am. Math. Mon."},{"key":"9367_CR21","first-page":"215","volume":"149","author":"PY Nie","year":"2004","unstructured":"Nie, P.Y.: A null space method for solving system of equations. Appl. Math. Comput. 149, 215\u2013226 (2004)","journal-title":"Appl. Math. Comput."},{"issue":"5","key":"9367_CR22","doi-asserted-by":"crossref","first-page":"993","DOI":"10.1137\/0715064","volume":"15","author":"GW Reddien","year":"1978","unstructured":"Reddien, G.W.: On Newton\u2019s method for singular problems. SIAM J. Numer. Anal. 15(5), 993\u2013996 (1978)","journal-title":"SIAM J. Numer. Anal."},{"key":"9367_CR23","doi-asserted-by":"crossref","first-page":"678","DOI":"10.1137\/S0036141003425003","volume":"36","author":"R Riaza","year":"2004","unstructured":"Riaza, R.: Attraction domains of degenerate singular equilibria in quasi-linear ODEs. SIAM J. Math. Anal. 36, 678\u2013690 (2004)","journal-title":"SIAM J. Math. Anal."},{"key":"9367_CR24","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1016\/j.jde.2005.06.009","volume":"217","author":"R Riaza","year":"2005","unstructured":"Riaza, R.: On the local classification of smooth maps induced by Newton\u2019s method. J. Differ. Equ. 217, 377\u2013392 (2005)","journal-title":"J. Differ. Equ."},{"key":"9367_CR25","doi-asserted-by":"crossref","first-page":"2242","DOI":"10.1016\/j.na.2007.01.055","volume":"68","author":"R Riaza","year":"2008","unstructured":"Riaza, R.: Local dynamics of quasilinear ODEs with folded singular equilibria. Nonlinear Anal. 68, 2242\u20132249 (2008)","journal-title":"Nonlinear Anal."},{"key":"9367_CR26","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1016\/S0377-0427(01)00404-6","volume":"140","author":"R Riaza","year":"2002","unstructured":"Riaza, R., Zufiria, P.J.: Discretization of implicit ODEs for singular root-finding problems. J. Comput. Appl. Math. 140, 695\u2013712 (2002)","journal-title":"J. Comput. Appl. Math."},{"key":"9367_CR27","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1137\/0721054","volume":"21","author":"RB Schnabel","year":"1984","unstructured":"Schnabel, R.B., Frank, P. D.: Tensor methods for nonlinear equations. SIAM J. Numer. Anal. 21, 815\u2013843 (1984)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"9367_CR28","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1016\/j.apnum.2004.09.029","volume":"54","author":"Y-Q Shen","year":"2005","unstructured":"Shen, Y.-Q., Ypma, T.J.: Newton\u2019s method for singular nonlinear equations using approximate left and right nullspaces of the Jacobian. Appl. Numer. Math. 54(2),256\u2013265 (2005)","journal-title":"Appl. Numer. Math."},{"key":"9367_CR29","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/BF02684472","volume":"58","author":"E Spedicato","year":"1997","unstructured":"Spedicato, E., Huang, Z.: Numerical experience with Newton-like methods for nonlinear algebraic systems. Computing 58, 69\u201389 (1997)","journal-title":"Computing"},{"key":"9367_CR30","unstructured":"Thomas, S.: Sequential Estimation Techniques For Quasi-Newton Algorithms, Ph.D. thesis, TR 75-227, Cornell University (1975)"},{"key":"9367_CR31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0377-0427(00)00417-9","volume":"124","author":"T Yamamoto","year":"2000","unstructured":"Yamamoto, T.: Historical developments in convergence analysis for Newton\u2019s and Newton-like methods. J. Comput. Appl. Math. 124, 1\u201323 (2000)","journal-title":"J. Comput. Appl. Math."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-010-9367-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-010-9367-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-010-9367-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T01:08:14Z","timestamp":1559351294000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-010-9367-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,2,6]]},"references-count":31,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2010,12]]}},"alternative-id":["9367"],"URL":"https:\/\/doi.org\/10.1007\/s11075-010-9367-z","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,2,6]]}}}