# On the high convergence orders of the Newton-GMBACK methods

## Abstract

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.

## Authors

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

## Keywords

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.

Scanned paper.

1222-9024

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