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On the convergence of the secant method under the gamma condition

100%

Argyros I.

Open Mathematics

2007

tom 5

nr 2

205-214

We provide sufficient convergence conditions for the Secant method of approximating a locally unique solution of an operator equation in a Banach space. The main hypothesis is the gamma condition first introduced in [10] for the study of Newton’s method. Our sufficient convergence condition reduces to the one obtained in [10] for Newton’s method. A numerical example is also provided.

A refined Newton’s mesh independence principle for a class of optimal shape design problems

100%

Argyros I.

Open Mathematics

2006

tom 4

nr 4

562-572

Shape optimization is described by finding the geometry of a structure which is optimal in the sense of a minimized cost function with respect to certain constraints. A Newton’s mesh independence principle was very efficiently used to solve a certain class of optimal design problems in [6]. Here motivated by optimization considerations we show that under the same computational cost an even finer mesh independence principle can be given.

Ograniczanie wyników

2 Open Mathematics

2 Argyros I.

1 2007

1 2006

Wyniki wyszukiwania

On the convergence of the secant method under the gamma condition

A refined Newton’s mesh independence principle for a class of optimal shape design problems