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Volumn 170, Issue 1, 2005, Pages 686-705

Convergence of Gauss-Newton's method and uniqueness of the solution

Author keywords

Convergence ball; Gauss Newton's method; Lipschitz condition; Uniqueness ball

Indexed keywords

APPROXIMATION THEORY; DERIVATIVES; ESTIMATION; PROBLEM SOLVING;

EID: 26844463954     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2004.12.055     Document Type: Article
Times cited : (46)

References (16)
  • 1
    • 0034546528 scopus 로고    scopus 로고
    • Historical developments in convergence analysis for Newton's and Newton-like methods
    • T. Yamamoto Historical developments in convergence analysis for Newton's and Newton-like methods J. Comput. Appl. Math. 124 2000 1 23
    • (2000) J. Comput. Appl. Math. , vol.124 , pp. 1-23
    • Yamamoto, T.1
  • 2
    • 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 1960 33 45
    • (1960) SIAM J. Appl. Math. , vol.17 , pp. 33-45
    • Stewart, G.W.1
  • 3
    • 0001470741 scopus 로고
    • The Newton-Kantorovich method under mild differentiability conditions and the Ptak estimates
    • I.K. Argyros The Newton-Kantorovich method under mild differentiability conditions and the Ptak estimates Monatsch. Math. 101 1990 175 193
    • (1990) Monatsch. Math. , vol.101 , pp. 175-193
    • Argyros, I.K.1
  • 4
    • 0001298745 scopus 로고    scopus 로고
    • On Newton's method under mild differentiability conditions and applications
    • I.k. Argyros On Newton's method under mild differentiability conditions and applications Appl. Math. Comput. 102 1999 177 183
    • (1999) Appl. Math. Comput. , vol.102 , pp. 177-183
    • Argyros, I.K.1
  • 5
    • 0018456412 scopus 로고
    • Covergence and complexity of Newton iteration
    • J.F. Traub, and H. Wozniakowski Covergence and complexity of Newton iteration J. Assoc. Comput. Math. 29 1979 250 258
    • (1979) J. Assoc. Comput. Math. , vol.29 , pp. 250-258
    • Traub, J.F.1    Wozniakowski, H.2
  • 7
    • 0000195992 scopus 로고
    • Perturbation theory for pseudo-inverse
    • P.A. Wedin Perturbation theory for pseudo-inverse BIT 13 1973 217 232
    • (1973) BIT , vol.13 , pp. 217-232
    • Wedin, P.A.1
  • 8
    • 84966209344 scopus 로고
    • The fundamental theorem of algebra and complexity theory
    • S. Smale The fundamental theorem of algebra and complexity theory Bull. Amer. Math. Soc. 4 1981 1 36
    • (1981) Bull. Amer. Math. Soc. , vol.4 , pp. 1-36
    • Smale, S.1
  • 10
    • 85011523909 scopus 로고    scopus 로고
    • Complexity theroy and numerical analysis
    • S. Smale Complexity theroy and numerical analysis Acta Numer. 6 1997 523 551
    • (1997) Acta Numer. , vol.6 , pp. 523-551
    • Smale, S.1
  • 11
    • 0039381062 scopus 로고
    • Affine invariant convergence results for Newton's method
    • T.J. Ypina Affine invariant convergence results for Newton's method BIT 22 1982 108 118
    • (1982) BIT , vol.22 , pp. 108-118
    • Ypina, T.J.1
  • 13
    • 0038932662 scopus 로고    scopus 로고
    • Covergence of Newton's method and inverse function in Banach space
    • X. Wang Covergence of Newton's method and inverse function in Banach space Math. Comput. 68 1999 169 186
    • (1999) Math. Comput. , vol.68 , pp. 169-186
    • Wang, X.1
  • 14
    • 0034348775 scopus 로고    scopus 로고
    • Covergence of Newton's method and uniqueness of the solution of equations in Banach space
    • X. Wang Covergence of Newton's method and uniqueness of the solution of equations in Banach space IMA J. Numer. Anal. 20 2000 123 134
    • (2000) IMA J. Numer. Anal. , vol.20 , pp. 123-134
    • Wang, X.1
  • 15
    • 0007167706 scopus 로고
    • A Kantorrovich-type convergence analysis for the Guass-Newton method
    • W.M. Haüßler A Kantorrovich-type convergence analysis for the Guass-Newton method Numer. Math. 48 1986 119 125
    • (1986) Numer. Math. , vol.48 , pp. 119-125
    • Haüßler, W.M.1
  • 16
    • 21344485372 scopus 로고
    • Convergence of Newton-like methods for singular operator equations using outer inverses
    • M.Z. Nashed, and X. Chen Convergence of Newton-like methods for singular operator equations using outer inverses Numer. Math. 66 1993 235 257
    • (1993) Numer. Math. , vol.66 , pp. 235-257
    • Nashed, M.Z.1    Chen, X.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.