Hybrid procedures for solving linear systems |
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Authors: | C Brezinski M Redivo-Zaglia |
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Institution: | (1) Laboratoire d'Analyse Num\'erique et d'Optimisation, UFR IEEA - M3, Universit\'e des Sciences et Technologies de Lille, F-59655 Villeneuve d'Ascq Cedex, France , FR;(2) Dipartimento di Elettronica e Informatica, Universit\`a degli Studi di Padova, via Gradenigo 6/a, I-35131 Padova, Italy , IT |
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Abstract: | Summary.
In this paper, we introduce the notion of hybrid procedures for solving a
system of linear equations. A hybrid procedure consists in a combination of
two arbitrary approximate solutions with coefficients summing
up to one. Thus
the combination only depends on one parameter whose value is chosen
in order to minimize the Euclidean norm of the residual vector obtained by
the hybrid procedure.
Properties of such procedures are studied in detail. The two approximate
solutions which are combined in a hybrid procedure are usually obtained
by two iterative methods. Several strategies for combining these two
methods together or with the previous iterate of the hybrid procedure itself
are discussed and their properties are analyzed.
Numerical experiments illustrate the various procedures.
Received October 21, 1992/Revised version
received May 28, 1993 |
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Keywords: | Mathematics Subject Classification (1991):65F05 65B05 |
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