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A unifying convergence analysis of Newton's method for twice Fréchet-differentiable operators

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Argyros I., González D.

Applicationes Mathematicae

2015

tom 42

nr 1

29-56

We provide a local as well as a semilocal convergence analysis for Newton's method using unifying hypotheses on twice Fréchet-differentiable operators in a Banach space setting. Our approach extends the applicability of Newton's method. Numerical examples are also provided.

Inexact Newton method under weak and center-weak Lipschitz conditions

100%

Argyros I., Khattri S.

Applicationes Mathematicae

2013

tom 40

nr 2

237-258

The paper develops semilocal convergence of Inexact Newton Method INM for approximating solutions of nonlinear equations in Banach space setting. We employ weak Lipschitz and center-weak Lipschitz conditions to perform the error analysis. The results obtained compare favorably with earlier ones in at least the case of Newton's Method (NM). Numerical examples, where our convergence criteria are satisfied but the earlier ones are not, are also explored.

Ograniczanie wyników

2 Applicationes Mathematicae

2 Argyros I.

1 González D.

1 Khattri S.

1 2015

1 2013

Wyniki wyszukiwania

A unifying convergence analysis of Newton's method for twice Fréchet-differentiable operators

Inexact Newton method under weak and center-weak Lipschitz conditions