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Semilocal convergence theorems for a certain class of iterative procedures

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Abstract

We provide semilocal convergence theorems for Newton-like methods in Banach space using outer and generalized inverses. In contrast to earlier results we use hypotheses on the second instead of the first Fréchet-derivative. This way our Newton-Kantorovich hypotheses differ from earlier ones. Our results can be used to solve undetermined systems, nonlinear least square problems and ill-posed nonlinear operator equations.

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References

  1. I. K. Argyros, On the solution of undetermined systems of nonlinear equations in Euclidean spaces,Pure Math. Appl. (PUMA) 4, 3 (1993), 199–209.

    MATH  Google Scholar 

  2. I. K. Argyros, On the convergence of inexact Newton-like methods,Public. Math. Debrecen 43, (1 and 2) (1993), 79–85.

    MATH  Google Scholar 

  3. I. K. Argyros, A convergence theorem for Newton-like methods under generalized Chen-Yamamoto-type assumptions,Appl. Math. Comput. 61, 1 (1994), 25–37.

    Article  MATH  MathSciNet  Google Scholar 

  4. I. K. Argyros, A unified approach for constructing fast two-step Newton-like methods,Mh. Math. 119 (1995), 1–22.

    Article  MATH  Google Scholar 

  5. I. K. Argyros and F. Szidarovszky,The Theory and Application of Iteration Methods, CRC Press, Inc., Boca Raton, Florida, U.S.A., 1993.

    Google Scholar 

  6. I. K. Argyros, Comparing the radii of some balls appearing in connection to three local convergence theorems for Newton’s method,Southwest Journal of Pure App. Math. 1 (1998).

  7. A. Ben-Israel and T. N. E. Greville,Generalized Inverses: Theory and Applications, John Wiley and Sons, New York, 1974.

    MATH  Google Scholar 

  8. X. Chen and M. Z. Nashed, Convergence of Newton-like methods for singular operator equations using outer inverses,Numer. Math. 66 (1993), 235–257.

    Article  MATH  MathSciNet  Google Scholar 

  9. P. Deuflhard and G. Heindl, Affine invariant convergence theorems for Newton’s method and extensions to related methods,SIAM J. Numer. Anal. 16 (1979), 1–10.

    Article  MATH  MathSciNet  Google Scholar 

  10. L. V. Kantorovich and G. P. Akilov,Functional Analysis, Pergamon Press, Oxford, 1982.

    MATH  Google Scholar 

  11. M. Z. Nashed, Inner, outer and generalized inverses in Banach and Hilbert spaces,Numer. Funct. Anal. Optimiz. 9 (1987), 261–325.

    Article  MATH  MathSciNet  Google Scholar 

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  1. Department of Mathematics, Cameron University, 73505, Lawton, IK

    Ioannis K. Argyros

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  1. Ioannis K. Argyros
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Argyros, I.K. Semilocal convergence theorems for a certain class of iterative procedures. Korean J. Comput. & Appl. Math 7, 29–40 (2000). https://doi.org/10.1007/BF03009926

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  • DOI: https://doi.org/10.1007/BF03009926

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