A new method based on generalized Taylor expansion for computing a series solution of the linear systems

In this paper, based on the generalized Taylor expansion and using the iteration matrix G of the iterative methods, we introduce a new method for computing a series solution of the linear systems. This method can be used to accelerate the convergence of the basic iterative methods. In addition, we s...

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Veröffentlicht in:	Applied mathematics and computation 2014-12, Vol.248, p.602-609
Hauptverfasser:	Toutounian, F., Nasabzadeh, H.
Format:	Artikel
Sprache:	eng
Schlagworte:	Basic iterative method Computation Construction Convergence Generalized Taylor expansion Intervals Iterative methods Linear system Linear systems Mathematical analysis Mathematical models Spectral radius
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container_title	Applied mathematics and computation
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creator	Toutounian, F. Nasabzadeh, H.
description	In this paper, based on the generalized Taylor expansion and using the iteration matrix G of the iterative methods, we introduce a new method for computing a series solution of the linear systems. This method can be used to accelerate the convergence of the basic iterative methods. In addition, we show that, by applying the new method to a divergent iterative scheme, it is possible to construct a convergent series solution and to find the convergence intervals of control parameter for special cases. Numerical experiments are given to show the efficiency of the new method.
doi_str_mv	10.1016/j.amc.2014.10.003
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subjects	Basic iterative method Computation Construction Convergence Generalized Taylor expansion Intervals Iterative methods Linear system Linear systems Mathematical analysis Mathematical models Spectral radius
title	A new method based on generalized Taylor expansion for computing a series solution of the linear systems
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