ALAMT  Vol.4 No.3 , September 2014
On the FOM Algorithm for the Resolution of the Linear Systems Ax = b
Author(s) Mongi Benhamadou
ABSTRACT
In this paper, we propose another version of the full orthogonalization method (FOM) for the resolution of linear system Ax = b, based on an extended definition of Sturm sequence in the calculation of the determinant of an upper hessenberg matrix in o(n2). We will also give a new version of Givens method based on using a tensor product and matrix addition. This version can be used in parallel calculation.

Cite this paper
Benhamadou, M. (2014) On the FOM Algorithm for the Resolution of the Linear Systems Ax = b. Advances in Linear Algebra & Matrix Theory, 4, 156-171. doi: 10.4236/alamt.2014.43014.
References
[1]   Toumi, A. (2005) Utilisation des filtres de Tchebycheff et construction de préconditionneurs spéciaux pour l’accélération des methods de Krylov. Thèse No. 2296, de l’Institut National Polytechnique de Toulouse, France.

[2]   Saad, Y. (2000) Iterative Methods for Sparse Linear Systems. 2nd Edition, Society for Industrial and Applied Mathematics, Philadelphia.

[3]   Benhamadou, M. (2000) Développement d’outils en Programmation Linéaire et Analyse Numérique matricielle. Thèse No. 1955, de l’Université Paul Sabatier Toulouse 3, Toulouse, France.

[4]   Wilkinson, J.H. (1965) The Algebraic Eigenvalue Problem. Clarendon Press, Oxford.

[5]   Gastinel, N. (1966) Analyse Numérique Linéaire. Hermann, Paris.

[6]   Ciarlet, P.G. (1980) Introduction à l’Analyse Numérique Matricielle et à l’Optimisation. Masson, Paris.

[7]   Lascaux, P. and Théodor, R. (1993) Analyse Numérique Matricielle Appliquée à l’Art de l’Ingénieur. Tome 1, Tome 2, Masson, Paris.

[8]   Jennings, A. (1980) Matrix Computation for Engineers and Scientists. John Wiley and Sons, Chichester.

[9]   Gregory, R.T. and Karney, D.L. (1969) A Collection of Matrices for Testing Computational Algorithms. Wiley-Inter-science, John Wiley & Sons, New York, London , Sydney, Toronto.

 
 
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