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Volumn 27, Issue 1, 2011, Pages 111-125

Local convergence analysis of the GaussNewton method under a majorant condition

Author keywords

GaussNewton method; Local convergence; Majorant condition; Nonlinear least squares problems

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS;

EID: 78649730612     PISSN: 0885064X     EISSN: 10902708     Source Type: Journal    
DOI: 10.1016/j.jco.2010.09.001     Document Type: Article
Times cited : (54)

References (25)
  • 1
    • 0345447647 scopus 로고    scopus 로고
    • Newton's method on Riemannian manifolds and a geometric model for the human spine
    • R.L. Adler, J.P. Dedieu, J.Y. Margulies, M. Martens, and M. Shub Newton's method on Riemannian manifolds and a geometric model for the human spine IMA J. Numer. Anal. 22 3 2002 359 390
    • (2002) IMA J. Numer. Anal. , vol.22 , Issue.3 , pp. 359-390
    • Adler, R.L.1    Dedieu, J.P.2    Margulies, J.Y.3    Martens, M.4    Shub, M.5
  • 2
    • 44649117065 scopus 로고    scopus 로고
    • A unifying local convergence result for Newton's method in Riemannian manifolds
    • F. Alvarez, J. Bolte, and J. Munier A unifying local convergence result for Newton's method in Riemannian manifolds Found. Comput. Math. 8 2 2008 197 226
    • (2008) Found. Comput. Math. , vol.8 , Issue.2 , pp. 197-226
    • Alvarez, F.1    Bolte, J.2    Munier, J.3
  • 3
    • 77955712562 scopus 로고    scopus 로고
    • Improved generalized differentiability conditions for Newton-like methods
    • I.K. Argyros, and S. Hilout Improved generalized differentiability conditions for Newton-like methods J. Complexity 22 3 2010 316 333
    • (2010) J. Complexity , vol.22 , Issue.3 , pp. 316-333
    • Argyros, I.K.1    Hilout, S.2
  • 5
    • 41549163866 scopus 로고    scopus 로고
    • The convergence analysis of inexact GaussNewton methods for nonlinear problems
    • J. Chen The convergence analysis of inexact GaussNewton methods for nonlinear problems Comput. Optim. Appl. 40 1 2008 97 118
    • (2008) Comput. Optim. Appl. , vol.40 , Issue.1 , pp. 97-118
    • Chen, J.1
  • 6
    • 26844463954 scopus 로고    scopus 로고
    • Convergence of GaussNewton's method and uniqueness of the solution
    • J. Chen, and W. Li Convergence of GaussNewton's method and uniqueness of the solution Appl. Math. Comput. 170 1 2005 686 705
    • (2005) Appl. Math. Comput. , vol.170 , Issue.1 , pp. 686-705
    • Chen, J.1    Li, W.2
  • 7
    • 33644860884 scopus 로고    scopus 로고
    • Convergence behaviour of inexact Newton methods under weak Lipschitz condition
    • J. Chen, and W. Li Convergence behaviour of inexact Newton methods under weak Lipschitz condition J. Comput. Appl. Math. 191 1 2006 143 164
    • (2006) J. Comput. Appl. Math. , vol.191 , Issue.1 , pp. 143-164
    • Chen, J.1    Li, W.2
  • 8
    • 0036228627 scopus 로고    scopus 로고
    • Newton's method for analytic systems of equations with constant rank derivatives
    • J.P. Dedieu, and M.H. Kim Newton's method for analytic systems of equations with constant rank derivatives J. Complexity 18 1 2002 187 209
    • (2002) J. Complexity , vol.18 , Issue.1 , pp. 187-209
    • Dedieu, J.P.1    Kim, M.H.2
  • 9
    • 0242323292 scopus 로고    scopus 로고
    • Newton's method on Riemannian manifolds: Covariant alpha theory
    • DOI 10.1093/imanum/23.3.395
    • J.P. Dedieu, P. Priouret, and G. Malajovich Newton's method on Riemannian manifolds: covariant alpha theory IMA J. Numer. Anal. 23 3 2003 395 419 (Pubitemid 37445939)
    • (2003) IMA Journal of Numerical Analysis , vol.23 , Issue.3 , pp. 395-419
    • Dedieu, J.-P.1    Priouret, P.2    Malajovich, G.3
  • 10
    • 0034409755 scopus 로고    scopus 로고
    • Newton's method for overdetermined systems of equations
    • J.P. Dedieu, and M. Shub Newton's method for overdetermined systems of equations Math. Comp. 69 231 2000 1099 1115
    • (2000) Math. Comp. , vol.69 , Issue.231 , pp. 1099-1115
    • Dedieu, J.P.1    Shub, M.2
  • 11
    • 0003315567 scopus 로고    scopus 로고
    • Numerical methods for unconstrained optimization and nonlinear equations
    • Society for Industrial and Applied Mathematics (SIAM) Philadelphia, PA
    • J.E. Dennis Jr., and R.B. Schnabel Numerical methods for unconstrained optimization and nonlinear equations Classics in Applied Mathematics vol. 16 1996 Society for Industrial and Applied Mathematics (SIAM) Philadelphia, PA Corrected reprint of the 1983 original
    • (1996) Classics in Applied Mathematics , vol.16
    • Dennis, Jr.J.E.1    Schnabel, R.B.2
  • 12
    • 67651149924 scopus 로고    scopus 로고
    • Local convergence of Newton's method in Banach space from the viewpoint of the majorant principle
    • O.P. Ferreira Local convergence of Newton's method in Banach space from the viewpoint of the majorant principle IMA J. Numer. Anal. 29 3 2009 746 759
    • (2009) IMA J. Numer. Anal. , vol.29 , Issue.3 , pp. 746-759
    • Ferreira, O.P.1
  • 13
    • 78649720606 scopus 로고    scopus 로고
    • Local convergence analysis of inexact Newton-like methods under majorant condition
    • in press (doi:10.1007/s10589-009-9249-2)
    • O.P. Ferreira, M.L.N. Gonalves, Local convergence analysis of inexact Newton-like methods under majorant condition. Comput. Optim. Appl., in press (doi:10.1007/s10589-009-9249-2 ).
    • Comput. Optim. Appl.
    • Ferreira, O.P.1
  • 14
    • 58849149829 scopus 로고    scopus 로고
    • Kantorovich's majorants principle for Newton's method
    • O.P. Ferreira, and B.F. Svaiter Kantorovich's majorants principle for Newton's method Comput. Optim. Appl. 42 2 2009 213 229
    • (2009) Comput. Optim. Appl. , vol.42 , Issue.2 , pp. 213-229
    • Ferreira, O.P.1    Svaiter, B.F.2
  • 16
    • 0002865409 scopus 로고
    • The principle of the majorant and Newton's method
    • L.V. Kantorovich The principle of the majorant and Newton's method Doklady Akad. Nauk SSSR (N.S.) 76 1951 17 20
    • (1951) Doklady Akad. Nauk SSSR (N.S.) , vol.76 , pp. 17-20
    • Kantorovich, L.V.1
  • 17
    • 77955711940 scopus 로고    scopus 로고
    • Convergence behavior of GaussNewton's method and extensions of the Smale point estimate theory
    • C. Li, N. Hu, and J. Wang Convergence behavior of GaussNewton's method and extensions of the Smale point estimate theory J. Complexity 26 3 2010 268 295
    • (2010) J. Complexity , vol.26 , Issue.3 , pp. 268-295
    • Li, C.1    Hu, N.2    Wang, J.3
  • 18
    • 2542442365 scopus 로고    scopus 로고
    • Convergence and uniqueness properties of GaussNewton's method
    • C. Li, W.H. Zhang, and X.Q. Jin Convergence and uniqueness properties of GaussNewton's method Comput. Math. Appl. 47 67 2004 1057 1067
    • (2004) Comput. Math. Appl. , vol.47 , Issue.67 , pp. 1057-1067
    • Li, C.1    Zhang, W.H.2    Jin, X.Q.3
  • 20
    • 56949098628 scopus 로고    scopus 로고
    • General local convergence theory for a class of iterative processes and its applications to Newton's method
    • P.D. Proinov General local convergence theory for a class of iterative processes and its applications to Newton's method J. Complexity 25 1 2009 38 62
    • (2009) J. Complexity , vol.25 , Issue.1 , pp. 38-62
    • Proinov, P.D.1
  • 21
    • 71649115541 scopus 로고    scopus 로고
    • New general convergence theory for iterative processes and its applications to NewtonKantorovich type theorems
    • P.D. Proinov New general convergence theory for iterative processes and its applications to NewtonKantorovich type theorems J. Complexity 26 1 2010 3 42
    • (2010) J. Complexity , vol.26 , Issue.1 , pp. 3-42
    • Proinov, P.D.1
  • 23
    • 0013440801 scopus 로고
    • On the continuity of the generalized inverse
    • G.W. Stewart On the continuity of the generalized inverse SIAM J. Appl. Math. 17 1969 33 45
    • (1969) SIAM J. Appl. Math. , vol.17 , pp. 33-45
    • Stewart, G.W.1
  • 24
    • 0034348775 scopus 로고    scopus 로고
    • Convergence of Newton's method and uniqueness of the solution of equations in Banach space
    • X. Wang Convergence of Newton's method and uniqueness of the solution of equations in Banach space IMA J. Numer. Anal. 20 1 2000 123 134
    • (2000) IMA J. Numer. Anal. , vol.20 , Issue.1 , pp. 123-134
    • Wang, X.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.