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Volumn 18, Issue 1, 1998, Pages 37-56

On a new Newton-Mysovskii-type theorem with applications to inexact Newton-like methods and their discretizations

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; INTEGRAL EQUATIONS; MATHEMATICAL OPERATORS; NEWTON-RAPHSON METHOD;

EID: 0032378878     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/18.1.37     Document Type: Article
Times cited : (20)

References (17)
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  • 2
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    • A mesh independence principle for operator equations and their discretizations under mild differentiability conditions
    • ARGYROS, I. K. 1990 A mesh independence principle for operator equations and their discretizations under mild differentiability conditions. Computing 45, 265-268.
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    • Argyros, I.K.1
  • 3
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    • On the discretization of Newton-like methods
    • ARGYROS, I. K. 1994 On the discretization of Newton-like methods. Int. J. Comput. Math. 52, 161-170.
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    • Argyros, I.K.1
  • 4
    • 0008854050 scopus 로고
    • A unified approach for constructing fast two-step Newton-like methods
    • ARGYROS, I. K. 1995 A unified approach for constructing fast two-step Newton-like methods. Monatshefte für Mathematik 119, 1-22.
    • (1995) Monatshefte für Mathematik , vol.119 , pp. 1-22
    • Argyros, I.K.1
  • 7
    • 0024302091 scopus 로고
    • Convergence domains of certain iterative methods for solving nonlinear equations
    • CHEN, X., & YAMAMOTO, T. 1989 Convergence domains of certain iterative methods for solving nonlinear equations. Numer. Funct. Anal. Optimiz. 10, 37-48.
    • (1989) Numer. Funct. Anal. Optimiz. , vol.10 , pp. 37-48
    • Chen, X.1    Yamamoto, T.2
  • 8
    • 0001820687 scopus 로고
    • Affine invariant convergence theorems for Newton's method and extensions to related methods
    • DEAUFLHARD, P., & HEINDL, G. 1979 Affine invariant convergence theorems for Newton's method and extensions to related methods. SIAM J. Numer. Anal. 16, 1-10.
    • (1979) SIAM J. Numer. Anal. , vol.16 , pp. 1-10
    • Deauflhard, P.1    Heindl, G.2
  • 9
    • 0026940480 scopus 로고
    • Asymptotic mesh independence of Newton-Galerkin methods and a refined Mysovskii theorem
    • DEAUFLHARD, P., & POTRA, F. A. 1992 Asymptotic mesh independence of Newton-Galerkin methods and a refined Mysovskii theorem. SIAM J. Numer. Anal. 29, 1395-1412.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 1395-1412
    • Deauflhard, P.1    Potra, F.A.2
  • 10
    • 0343486320 scopus 로고
    • A fast multilevel algorithm for integral equations
    • KELLEY, C. T. 1995 A fast multilevel algorithm for integral equations. SIAM J. Numer. Anal. 32, 384-399.
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    • Kelley, C.T.1
  • 11
    • 0039851463 scopus 로고
    • On the convergence of Newton's method
    • In Russian
    • MYSOVSKII, I. 1949 On the convergence of Newton's method. Trudy Mat. Inst. Steklov 28, 145-147. (In Russian.)
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    • Mysovskii, I.1
  • 12
    • 0021585816 scopus 로고
    • On an iterative algorithm of order 1·839... For solving nonlinear operator equations
    • POTRA, F. A. 1984-85 On an iterative algorithm of order 1·839... for solving nonlinear operator equations. Numer. Funct. Anal. Optimiz. 7, 75-106.
    • (1984) Numer. Funct. Anal. Optimiz. , vol.7 , pp. 75-106
    • Potra, F.A.1
  • 13
    • 0002727081 scopus 로고
    • Sharp error bounds for Newton's process
    • POTRA, F. A., & PTAK, V. 1980 Sharp error bounds for Newton's process. Numer. Math. 34, 63-72.
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    • Potra, F.A.1    Ptak, V.2
  • 14
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    • The method of tangent hyperbolas
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  • 15
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    • YAMAMOTO, T. 1988 On the method of tangent hyperbolas in Banach spaces. J. Comput. Appl. Math. 21, 75-86.
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  • 17
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    • The majorant method in the theory of Newton-Kantorovich approximations and the Ptak error estimates
    • ZABREJKO, P. P., & NGUEN, D. F. 1987 The majorant method in the theory of Newton-Kantorovich approximations and the Ptak error estimates. Numer. Funct. Anal. Optimiz. 9, 671-684.
    • (1987) Numer. Funct. Anal. Optimiz. , vol.9 , pp. 671-684
    • Zabrejko, P.P.1    Nguen, D.F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.