Displaying similar documents to “Improved convergence bounds for smoothed aggregation method: linear dependence of the convergence rate on the number of levels”

Local convergence of a multi-step high order method with divided differences under hypotheses on the first derivative

Ioannis K. Argyros, Santhosh George (2017)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Similarity:

This paper is devoted to the study of a multi-step method with divided differences for solving nonlinear equations in Banach spaces. In earlier studies, hypotheses on the Fréchet derivative up to the sixth order of the operator under consideration is used to prove the convergence of the method. That restricts the applicability of the method. In this paper we extended the applicability of the sixth-order multi-step method by using only hypotheses on the first derivative of the operator...

Model analysis of BPX preconditioner based on smoothed aggregation

Pavla Fraňková, Jan Mandel, Petr Vaněk (2015)

Applications of Mathematics

Similarity:

We prove nearly uniform convergence bounds for the BPX preconditioner based on smoothed aggregation under the assumption that the mesh is regular. The analysis is based on the fact that under the assumption of regular geometry, the coarse-space basis functions form a system of macroelements. This property tends to be satisfied by the smoothed aggregation bases formed for unstructured meshes.

Local convergence comparison between two novel sixth order methods for solving equations

Santhosh George, Ioannis K. Argyros (2019)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Similarity:

The aim of this article is to provide the local convergence analysis of two novel competing sixth convergence order methods for solving equations involving Banach space valued operators. Earlier studies have used hypotheses reaching up to the sixth derivative but only the first derivative appears in these methods. These hypotheses limit the applicability of the methods. That is why we are motivated to present convergence analysis based only on the first derivative. Numerical examples...

Local convergence for a family of iterative methods based on decomposition techniques

Ioannis K. Argyros, Santhosh George, Shobha Monnanda Erappa (2016)

Applicationes Mathematicae

Similarity:

We present a local convergence analysis for a family of iterative methods obtained by using decomposition techniques. The convergence of these methods was shown before using hypotheses on up to the seventh derivative although only the first derivative appears in these methods. In the present study we expand the applicability of these methods by showing convergence using only the first derivative. Moreover we present a radius of convergence and computable error bounds based only on Lipschitz...