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The effect of rounding errors on a certain class of iterative methods

Ioannis Argyros (2000)

Applicationes Mathematicae

In this study we are concerned with the problem of approximating a solution of a nonlinear equation in Banach space using Newton-like methods. Due to rounding errors the sequence of iterates generated on a computer differs from the sequence produced in theory. Using Lipschitz-type hypotheses on the mth Fréchet derivative (m ≥ 2 an integer) instead of the first one, we provide sufficient convergence conditions for the inexact Newton-like method that is actually generated on the computer. Moreover,...

The fourth order accuracy decomposition scheme for an evolution problem

Zurab Gegechkori, Jemal Rogava, Mikheil Tsiklauri (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In the present work, the symmetrized sequential-parallel decomposition method with the fourth order accuracy for the solution of Cauchy abstract problem with an operator under a split form is presented. The fourth order accuracy is reached by introducing a complex coefficient with the positive real part. For the considered scheme, the explicit a priori estimate is obtained.

The fourth order accuracy decomposition scheme for an evolution problem

Zurab Gegechkori, Jemal Rogava, Mikheil Tsiklauri (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In the present work, the symmetrized sequential-parallel decomposition method with the fourth order accuracy for the solution of Cauchy abstract problem with an operator under a split form is presented. The fourth order accuracy is reached by introducing a complex coefficient with the positive real part. For the considered scheme, the explicit a priori estimate is obtained.

The norm convergence of a Magnus expansion method

András Bátkai, Eszter Sikolya (2012)

Open Mathematics

We consider numerical approximation to the solution of non-autonomous evolution equations. The order of convergence of the simplest possible Magnus method is investigated.

The Perturbed Generalized Tikhonov's Algorithm

Alexandre, P. (1999)

Serdica Mathematical Journal

We work on the research of a zero of a maximal monotone operator on a real Hilbert space. Following the recent progress made in the context of the proximal point algorithm devoted to this problem, we introduce simultaneously a variable metric and a kind of relaxation in the perturbed Tikhonov’s algorithm studied by P. Tossings. So, we are led to work in the context of the variational convergence theory.

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