메뉴 건너뛰기




Volumn 50, Issue 3, 2000, Pages 603-614

Local convergence theorems of Newton's method for nonlinear equations using outer or generalized inverses

Author keywords

Banach space; Fr chet derivative; Generalized inverse; Local convergence; Newton's method; Outer inverse

Indexed keywords


EID: 0035648886     PISSN: 00114642     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022893812726     Document Type: Article
Times cited : (6)

References (14)
  • 2
    • 0007239131 scopus 로고
    • On the solution of undetermined systems of nonlinear equations in euclidean spaces
    • I. K. Argyros: On the solution of undetermined systems of nonlinear equations in Euclidean spaces. Pure Math. Appl. 4, 3 (1993), 199-209.
    • (1993) Pure Math. Appl. , vol.4 , Issue.3 , pp. 199-209
    • Argyros, I.K.1
  • 3
    • 0007233149 scopus 로고
    • On the discretization of Newton-like methods
    • I. K. Argyros: On the discretization of Newton-like methods. Int. J. Comput. Math. 52 (1994), 161-170.
    • (1994) Int. J. Comput. Math. , vol.52 , pp. 161-170
    • Argyros, I.K.1
  • 4
    • 0007233150 scopus 로고    scopus 로고
    • Comparing the radii of some balls appearing in connection to three local convergence theorems for Newton's method
    • I. K. Argyros: Comparing the radii of some balls appearing in connection to three local convergence theorems for Newton's method. Southwest J. Pure Appl. Math. 1 (1998).
    • (1998) Southwest J. Pure Appl. Math. , vol.1
    • Argyros, I.K.1
  • 5
    • 0007240585 scopus 로고    scopus 로고
    • Semilocal convergence theorems for a certain class of iterative procedures using outer or generalized inverses and hypotheses on the second fréchet-derivative
    • I. K. Argyros: Semilocal convergence theorems for a certain class of iterative procedures using outer or generalized inverses and hypotheses on the second Fréchet-derivative. Korean J. Comput. Appl. Math. 6 (1999).
    • (1999) Korean J. Comput. Appl. Math. , vol.6
    • Argyros, I.K.1
  • 7
    • 0000617516 scopus 로고
    • A Newton-Raphson method for the solution of equations
    • A. Ben-Israel: A Newton-Raphson method for the solution of equations. J Math Anal Appl. 15 (1966), 243-253.
    • (1966) J Math Anal Appl. , vol.15 , pp. 243-253
    • Ben-Israel, A.1
  • 9
    • 21344485372 scopus 로고
    • Convergence of Newton-like methods for singular operator equations using outer inverses
    • X. Chen, M. Z. Nashed: 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
    • Chen, X.1    Nashed, M.Z.2
  • 10
    • 0031531517 scopus 로고    scopus 로고
    • Convergence of Newton's method for singular and nonsmooth equations using outer inverses
    • X. Chen, M. Z. Nashed, L. Qi: Convergence of Newton's method for singular and nonsmooth equations using outer inverses. SIAM J. Optim. 7 (1997), 445-462.
    • (1997) SIAM J. Optim. , vol.7 , pp. 445-462
    • Chen, X.1    Nashed, M.Z.2    Qi, L.3
  • 11
    • 0001820687 scopus 로고
    • Affine invariant convergence theorems for Newton's method and extensions to related methods
    • P. Deuflhard, G. Heindl: 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
  • 12
    • 0007167706 scopus 로고
    • A kantorovich-type convergence analysis for the Gauss-Newton method
    • W. M. Häubler: A Kantorovich-type convergence analysis for the Gauss-Newton method. Numer. Math. 48 (1986), 119-125.
    • (1986) Numer. Math. , vol.48 , pp. 119-125
    • Häubler, W.M.1
  • 14
    • 0007163216 scopus 로고
    • Inner, outer and generalized inverses in Banach and Hilbert spaces
    • M. Z. Nashed: Inner, outer and generalized inverses in Banach and Hilbert spaces. Numer. Funct. Anal. Optim. 9 (1987), 261-325.
    • (1987) Numer. Funct. Anal. Optim. , vol.9 , pp. 261-325
    • Nashed, M.Z.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.