Displaying similar documents to “Efficient inexact Newton-like methods with application to problems of the deformation theory of plasticity”

Operator preconditioning with efficient applications for nonlinear elliptic problems

Janos Karátson (2012)

Open Mathematics

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This paper is devoted to the numerical solution of nonlinear elliptic partial differential equations. Such problems describe various phenomena in science. An approach that exploits Hilbert space theory in the numerical study of elliptic PDEs is the idea of preconditioning operators. In this survey paper we briefly summarize the main lines of this theory with various applications.

A comparison of some efficient numerical methods for a nonlinear elliptic problem

Balázs Kovács (2012)

Open Mathematics

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The aim of this paper is to compare and realize three efficient iterative methods, which have mesh independent convergence, and to propose some improvements for them. We look for the numerical solution of a nonlinear model problem using FEM discretization with gradient and Newton type methods. Three numerical methods have been carried out, namely, the gradient, Newton and quasi-Newton methods. We have solved the model problem with these methods, we have investigated the differences between...

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

Ioannis Argyros (2006)

Open Mathematics

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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.

A Note on the “Constructing” of Nonstationary Methods for Solving Nonlinear Equations with Raised Speed of Convergence

Kyurkchiev, Nikolay, Iliev, Anton (2009)

Serdica Journal of Computing

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This paper is partially supported by project ISM-4 of Department for Scientific Research, “Paisii Hilendarski” University of Plovdiv. In this paper we give methodological survey of “contemporary methods” for solving the nonlinear equation f(x) = 0. The reason for this review is that many authors in present days rediscovered such classical methods. Here we develop one methodological schema for constructing nonstationary methods with a preliminary chosen speed of convergence. ...

Discrete evolutions: Convergence and applications

Erich Bohl, Johannes Schropp (1993)

Applications of Mathematics

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We prove a convergence result for a time discrete process of the form x ( t + h ) - x ( t ) = h V ( h , x ( t + α 1 ( t ) h ) , . . . , x ( t + α L ( t ) h ) ) t = T + j h , j = 0 , . . . , σ ( h ) - 1 under weak conditions on the function V . This result is a slight generalization of the convergence result given in [5].Furthermore, we discuss applications to minimizing problems, boundary value problems and systems of nonlinear equations.