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The Gradient Method for Overdetermined Infinite Linear Systems

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Author(s): Bela Finta

Journal: Scientific Bulletin of the ''Petru Maior" University of Tîrgu Mureș
ISSN 1841-9267

Volume: 9 (XXVI);
Issue: 2;
Start page: 5;
Date: 2012;
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Keywords: gradient method | least squares method | infinite linear systems | overdetermined infinite linear systems | space l 2

ABSTRACT
It is well known the notion of overdetermined finite linear system and its solution in the sense of the least squares method (see for example [1], [7] or [8]). In [5] we presented the gradient method for overdetermined finite linear systems and in [6] we made the comparative efficiencies of the least square method and the gradient method for finite overdetermined linear systems. In [3] we considered the notion of overdetermines infinite linear system and its solution in the sense of the least squares method. In [4] we showed the complex variant of this result. The purpose of this paper is to extend the classical gradient method to overdetermined infinite linear systems.
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