Displaying similar documents to “On the convergence of approximate iterations for an abstract equation”

Numerical homogenization: survey, new results, and perspectives

Antoine Gloria (2012)

ESAIM: Proceedings

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These notes give a state of the art of numerical homogenization methods for linear elliptic equations. The guideline of these notes is analysis. Most of the numerical homogenization methods can be seen as (more or less different) discretizations of the same family of continuous approximate problems, which H-converges to the homogenized problem. Likewise numerical correctors may also be interpreted as approximations of Tartar’s correctors....

Altman's methods revisited

C. Roland, B. Beckermann, C. Brezinski (2004)

Applicationes Mathematicae

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We discuss two different methods of Altman for solving systems of linear equations. These methods can be considered as Krylov subspace type methods for solving a projected counterpart of the original system. We discuss the link to classical Krylov subspace methods, and give some theoretical and numerical results on their convergence behavior.

On numerical solution of ordinary differential equations with discontinuities

Tadeusz Jankowski (1988)

Aplikace matematiky

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The author defines the numerical solution of a first order ordinary differential equation on a bounded interval in the way covering the general form of the so called one-step methods, proves convergence of the method (without the assumption of continuity of the righthad side) and gives a sufficient condition for the order of convergence to be O ( h v ) .

On the convergence and application of Stirling's method

Ioannis K. Argyros (2003)

Applicationes Mathematicae

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We provide new sufficient convergence conditions for the local and semilocal convergence of Stirling's method to a locally unique solution of a nonlinear operator equation in a Banach space setting. In contrast to earlier results we do not make use of the basic restrictive assumption in [8] that the norm of the Fréchet derivative of the operator involved is strictly bounded above by 1. The study concludes with a numerical example where our results compare favorably with earlier ones. ...