On the semilocal convergence of a two-step Newton-like projection method for ill-posed equations

Volume 40 / 2013

Ioannis K. Argyros, Santhosh George Applicationes Mathematicae 40 (2013), 367-382 MSC: 65J20, 65J15, 65H10, 65G99, 47J35, 47H99, 49M15. DOI: 10.4064/am40-3-7


We present new semilocal convergence conditions for a two-step Newton-like projection method of Lavrentiev regularization for solving ill-posed equations in a Hilbert space setting. The new convergence conditions are weaker than in earlier studies. Examples are presented to show that older convergence conditions are not satisfied but the new conditions are satisfied.


  • Ioannis K. ArgyrosDepartment of Mathematical Sciences
    Cameron University
    Lawton, OK 73505, U.S.A.
  • Santhosh GeorgeDepartment of Mathematical
    and Computational Sciences
    National Institute of Technology
    Karnataka, India 757 025

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