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Volumn 157, Issue 1, 2003, Pages 169-185

An improved error analysis for Newton-like methods under generalized conditions

Author keywords

Banach space; Fr chet derivative; Majorant principle; Majorizing sequence; Newton Kantorovich hypothesis; Newton like method; Radius of convergence

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; INFORMATION ANALYSIS;

EID: 0043122981     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(03)00390-X     Document Type: Article
Times cited : (19)

References (15)
  • 1
    • 0032378878 scopus 로고    scopus 로고
    • On a new Newton-Mysovskii-type theorem with applications to inexact Newton-like methods and their discretizations
    • Argyros I.K. On a new Newton-Mysovskii-type theorem with applications to inexact Newton-like methods and their discretizations IMA J. Numer. Anal. 18 1997 37-56
    • (1997) IMA J. Numer. Anal. , vol.18 , pp. 37-56
    • Argyros, I.K.1
  • 2
    • 0041116657 scopus 로고    scopus 로고
    • Local convergence of inexact Newton-like iterative methods and applications
    • Argyros I.K. Local convergence of inexact Newton-like iterative methods and applications Comput. Math. Appl. 39 2000 69-75
    • (2000) Comput. Math. Appl. , vol.39 , pp. 69-75
    • Argyros, I.K.1
  • 5
    • 0024302091 scopus 로고
    • Convergence domains of certain iterative methods for solving nonlinear equations
    • Chen X. Yamamoto T. Convergence domains of certain iterative methods for solving nonlinear equations Numer. Funct. Anal. Optim. 10 1,2 1989 37-48
    • (1989) Numer. Funct. Anal. Optim. , vol.10 , Issue.1-2 , pp. 37-48
    • Chen, X.1    Yamamoto, T.2
  • 6
    • 0003207251 scopus 로고
    • Toward a unified convergence theory for Newton-like methods
    • L.B. Rall (Ed.), New York: Academic Press
    • Dennis J.E. Toward a unified convergence theory for Newton-like methods Rall L.B. Nonlinear Functional Analysis and Applications 1971 425-472 Academic Press New York
    • (1971) Nonlinear Functional Analysis and Applications , pp. 425-472
    • Dennis, J.E.1
  • 7
    • 0001820687 scopus 로고
    • Affine invariant convergence theorems for Newton's method and extensions to related methods
    • Deuflhard P. Heindl G. Affine invariant convergence theorems for Newton's method and extensions to related methods SIAM J. Numer. Anal. 16 1979 1-10
    • (1979) SIAM J. Numer. Anal. , vol.16 , pp. 1-10
    • Deuflhard, P.1    Heindl, G.2
  • 9
    • 84966239458 scopus 로고
    • Majorizing sequences and error bounds for iterative methods
    • Miel G.J. Majorizing sequences and error bounds for iterative methods Math. Comput. 34 149 1980 185-202
    • (1980) Math. Comput. , vol.34 , Issue.149 , pp. 185-202
    • Miel, G.J.1
  • 10
    • 0021313369 scopus 로고
    • A note on Newton-type iterative methods
    • Moret I. A note on Newton-type iterative methods Computing 33 1984 65-73
    • (1984) Computing , vol.33 , pp. 65-73
    • Moret, I.1
  • 11
    • 0042840798 scopus 로고
    • On the convergence of a class of Newton-like methods
    • Lecture Notes in Mathematics R. Ansarge, & W. Toening (Eds.), New York: Springer, Berlin, Heidelberg
    • Potra F.A. On the convergence of a class of Newton-like methods Ansarge R. Toening W. Iterative Solution of Nonlinear Systems of Equations Lecture Notes in Mathematics Vol. 953 1982 125-137 Springer, Berlin, Heidelberg New York
    • (1982) Iterative Solution of Nonlinear Systems of Equations , vol.953 , pp. 125-137
    • Potra, F.A.1
  • 12
    • 0002214493 scopus 로고
    • A unified convergence theory for a class of iterative processes
    • Rheinboldt W.C. A unified convergence theory for a class of iterative processes SIAM J. Numer. Anal. 5 1968 42-63
    • (1968) SIAM J. Numer. Anal. , vol.5 , pp. 42-63
    • Rheinboldt, W.C.1
  • 13
    • 0041338065 scopus 로고
    • An adaptive continuation process for solving systems of nonlinear equations
    • Rheinboldt W.C. An adaptive continuation process for solving systems of nonlinear equations Polish Acad. Sci. Banach Control Publ. 3 1977 129-142
    • (1977) Polish Acad. Sci. Banach Control Publ. , vol.3 , pp. 129-142
    • Rheinboldt, W.C.1
  • 14
    • 0041338068 scopus 로고
    • A convergence theorem for Newton-like methods in Banach spaces
    • Yamamoto T. A convergence theorem for Newton-like methods in Banach spaces Numer. Math. 51 1987 545-557
    • (1987) Numer. Math. , vol.51 , pp. 545-557
    • Yamamoto, T.1
  • 15
    • 0021446370 scopus 로고
    • Local convergence of inexact Newton methods
    • Ypma T.J. Local convergence of inexact Newton methods SIAM J. Numer. Anal. 21 3 1984 583-590
    • (1984) SIAM J. Numer. Anal. , vol.21 , Issue.3 , pp. 583-590
    • Ypma, T.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.