We show that a new sufficient condition for the convergence with q-order two of the inexact Newton iterates may be obtained by considering the normwise backward error of the approximate steps and a result on perturbed Newton methods. This condition is in fact equivalent to the characterization given by Dembo, Eisenstat and Steihaug.
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)
nonlinear system of equations in Rn; inexact Newton method; residual; local convergence; forcing term; q-convergence order.
E. Cătinaş, A note on the quadratic convergence of the inexact Newton methods, Rev. Anal. Numér. Théor. Approx., 29 (2000) no. 2, pp. 129-133.
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