On the r-convergence orders of the inexact perturbed Newton methods

The inexact perturbed Newton methods recently introduced by us are variant of Newton method, which assume that at each step the linear systems are perturbed, and then they are only approximately solved. The q-convergence orders of the iterates were characterized using the results of Dembo, Eisenstat and Steihaug on inexact Newton methods.

In this note we deduce, in the same manner, the characterization of the r-convergence orders of these iterates.

Emil Cătinaş
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

inexact perturbed Newton methods; nonlinear systems in Rn; convergence orders; r-convergence order; forcing terms.

Scanned paper (soon).

Latex version of the paper (soon).

E. Cătinaş, On the r-convergence orders of the inexact perturbed Newton methods, Bul. ştiinţ. Univ. Baia Mare, Ser. B, Mat. Inf., 15 (1999) no. 1-2, pp. 75-78.

Google Scholar citations

The definition of the R-convergence orders has been rigorously analyzed in the paper

• E. Cătinaş, A survey on the high convergence orders and computational convergence orders of sequences, Appl. Math. Comput., 343 (2019) 1-20.