{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T10:16:58Z","timestamp":1697969818923},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[1982,9,1]],"date-time":"1982-09-01T00:00:00Z","timestamp":399686400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computing"],"published-print":{"date-parts":[[1982,9]]},"DOI":"10.1007\/bf02241698","type":"journal-article","created":{"date-parts":[[2005,11,14]],"date-time":"2005-11-14T23:27:02Z","timestamp":1132010822000},"page":"201-226","source":"Crossref","is-referenced-by-count":55,"title":["A comparison of methods for determining turning points of nonlinear equations"],"prefix":"10.1007","volume":"29","author":[{"given":"R. G.","family":"Melhem","sequence":"first","affiliation":[]},{"given":"W. C.","family":"Rheinboldt","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"BF02241698_CR1","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/0771-050X(78)90015-3","volume":"4","author":"J. P. Abbott","year":"1978","unstructured":"Abbott, J. P.: An efficient algorithm for the determination of certain bifurcation points. J. of Comp. and Appl. Math.4, 19\u201327 (1978).","journal-title":"J. of Comp. and Appl. Math."},{"key":"BF02241698_CR2","volume-title":"Algorithms for minimization without derivatives","author":"R. P. Brent","year":"1973","unstructured":"Brent, R. P.: Algorithms for minimization without derivatives. Englewood Cliffs, N. J.: Prentice-Hall 1973."},{"key":"BF02241698_CR3","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1137\/0710031","volume":"10","author":"R. P. Brent","year":"1973","unstructured":"Brent, R. P.: Some efficient algorithms for solving systems of nonlinear equations. SIAM J. Num. Anal.10, 327\u2013344 (1973).","journal-title":"SIAM J. Num. Anal."},{"key":"BF02241698_CR4","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1137\/0706051","volume":"6","author":"K. M. Brown","year":"1969","unstructured":"Brown, K. M.: A quadratically convergent Newton-like method based on Gaussian elimination. SIAM J. Num. Anal.6, 560\u2013569 (1969).","journal-title":"SIAM J. Num. Anal."},{"key":"BF02241698_CR5","doi-asserted-by":"crossref","first-page":"550","DOI":"10.1145\/321186.321200","volume":"10","author":"F. Freudenstein","year":"1963","unstructured":"Freudenstein, F., Roth, B.: Numerical solution of systems of nonlinear equations. J. ACM10, 550\u2013556 (1963).","journal-title":"J. ACM"},{"key":"BF02241698_CR6","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1115\/1.3564770","volume":"36","author":"A. D. Kerr","year":"1969","unstructured":"Kerr, A. D., Soifer, M. T.: The linearization of the prebuckling state and its effect on the determining instability load. Trans. ASME J. of Applied Mech.36, 775\u2013783 (1969).","journal-title":"Trans. ASME J. of Applied Mech."},{"key":"BF02241698_CR7","doi-asserted-by":"crossref","first-page":"1439","DOI":"10.1016\/0009-2509(75)85078-0","volume":"30","author":"M. Kubicek","year":"1975","unstructured":"Kubicek, M., Hlavacek, V.: Solution of nonlinear boundary-value problems IX. Chem. Eng. Sci.30, 1439\u20131440 (1975).","journal-title":"Chem. Eng. Sci."},{"key":"BF02241698_CR8","unstructured":"Mau, S. T., Gallagher, R. H.: A finite element procedure for nonlinear prebuckling and initial postbuckling analysis. NASA Report, NASA-CR-1936. January 1972."},{"key":"BF02241698_CR9","unstructured":"Mehra, R. K., Kessel, W. C., Carroll, J. V.: Global stability and control analysis of aircraft at high angles of attack. ONR Report-CR-215-248-1, 2, 3, June 1977, 78, 79."},{"key":"BF02241698_CR10","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1137\/0717048","volume":"17","author":"G. Moore","year":"1980","unstructured":"Moore, G., Spence, A.: The calculation of turning points of nonlinear equations. SIAM J. Num. Anal.17, 567\u2013576 (1980).","journal-title":"SIAM J. Num. Anal."},{"key":"BF02241698_CR11","volume-title":"Finite elements of nonlinear continua","author":"J. T. Oden","year":"1972","unstructured":"Oden, J. T.: Finite elements of nonlinear continua. New York: McGraw-Hill 1972."},{"key":"BF02241698_CR12","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1007\/BF01400320","volume":"37","author":"J. C. Paumier","year":"1981","unstructured":"Paumier, J. C.: Une m\u00e9thode num\u00e9rique pour le calcul des points de retournement. Application \u00e0 un probl\u00e8me aux limites non-lin\u00e9aire. Num. Math.37, 433\u2013444 (1981).","journal-title":"Num. Math."},{"key":"BF02241698_CR13","unstructured":"P\u00f6nisch, G., Schwetlick, H.: Ein lokal \u00fcberlinear konvergentes Verfahren zur Bestimmung von R\u00fcckkehrpunkten implizit definierter Raumkurven. TU Dresden, Sektion Mathematik, Preprint 07-30-77, 1977; Num. Math. (in press)."},{"key":"BF02241698_CR14","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/BF02241778","volume":"26","author":"G. P\u00f6nisch","year":"1981","unstructured":"P\u00f6nisch, G., Schwetlick, H.: Computing turning points of curves implicity defined by nonlinear equations depending on a parameter. Computing26, 107\u2013121 (1981).","journal-title":"Computing"},{"key":"BF02241698_CR15","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1137\/0717020","volume":"17","author":"W. C. Rheinboldt","year":"1980","unstructured":"Rheinboldt, W. C.: Solution fields of nonlinear equations and continuation methods. SIAM J. Num. Anal.17, 221\u2013237 (1980).","journal-title":"SIAM J. Num. Anal."},{"key":"BF02241698_CR16","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1137\/0719046","volume":"19","author":"W. C. Rheinboldt","year":"1982","unstructured":"Rheinboldt, W. C.: Computation of critical boundaries on equilibrium manifolds. Univ. of Pittsburgh, Inst. for Computational Math. and Appl., Techn. Rept. ICMA-80-20, 1980, SIAM J. Num. Anal.19, 653\u2013669 (1982).","journal-title":"SIAM J. Num. Anal."},{"key":"BF02241698_CR17","unstructured":"Rheinboldt, W. C., Burkardt, J. V.: A program for a locally-parametrized continuation process. Univ. of Pittsburgh, Inst. for Computational Math. and Appl., Techn. Rept. ICMA-81-30, 1981; ACM-TOMS (submitted for publication)."},{"key":"BF02241698_CR18","unstructured":"Schwetlick, H.: Effective methods for computing turning points of curves implicitly defined by nonlinear equations. Martin Luther Universit\u00e4t, Halle-Wittenberg, Sektion Mathem., Preprint No. 46, 1981."},{"key":"BF02241698_CR19","doi-asserted-by":"crossref","first-page":"375","DOI":"10.2514\/3.58787","volume":"14","author":"A. A. Schy","year":"1977","unstructured":"Schy, A. A., Hannah, M. E.: Prediction of jump phenomena in roll-coupled maneuvers of airplanes. J. of Aircraft14, 375\u2013382 (1977).","journal-title":"J. of Aircraft"},{"key":"BF02241698_CR20","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/BF01398649","volume":"33","author":"R. Seydel","year":"1979","unstructured":"Seydel, R.: Numerical computation of branch points in nonlinear equations. Numer. Math.33, 339\u2013352 (1979).","journal-title":"Numer. Math."},{"key":"BF02241698_CR21","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1137\/0712034","volume":"12","author":"R. B. Simpson","year":"1975","unstructured":"Simpson, R. B.: A method for numerical determination of bifurcation states of nonlinear systems of equations. SIAM J. Num. Anal.12, 439\u2013451 (1975).","journal-title":"SIAM J. Num. Anal."},{"key":"BF02241698_CR22","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/0020-7683(69)90023-7","volume":"5","author":"A. C. Walker","year":"1969","unstructured":"Walker, A. C.: A non-linear finite element analysis of shallow circular arches. Int. f. Solids Structures5, 97\u2013107 (1969).","journal-title":"Int. f. Solids Structures"},{"key":"BF02241698_CR23","doi-asserted-by":"crossref","first-page":"26","DOI":"10.2514\/3.55740","volume":"1","author":"J. W. Young","year":"1978","unstructured":"Young, J. W., Schy, A. A., Johnson, K. G.: Prediction of jump phenomena in aircraft maneuvers, including nonlinear aerodynamic effects. J. of Guidance and Control1, 26\u201331 (1978).","journal-title":"J. of Guidance and Control"}],"container-title":["Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02241698.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02241698\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02241698","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,14]],"date-time":"2019-05-14T19:15:45Z","timestamp":1557861345000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02241698"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,9]]},"references-count":23,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1982,9]]}},"alternative-id":["BF02241698"],"URL":"https:\/\/doi.org\/10.1007\/bf02241698","relation":{},"ISSN":["0010-485X","1436-5057"],"issn-type":[{"value":"0010-485X","type":"print"},{"value":"1436-5057","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,9]]}}}