GMBACK is a Krylov solver for linear systems in \(\mathbb{R}^n\).

We analyze here the high convergence orders (superlinear convergence) of the Newton-GMBACK methods, which can be characterized applying three different existing results.

In this note we show by some direct calculations that these characterizations are equivalent.


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


nonlinear system of equations in Rn; inexact Newton method; Krylov methods; linear systems of equation in Rn; residual; local convergence; superlinear convergence.

Cite this paper as:

E. Cătinaş, On the high convergence orders of the Newton-GMBACK methods, Rev. Anal. Numér. Théor. Approx., 28 (1999) no. 2, pp. 125-132.


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