Back
 ALAMT  Vol.4 No.3 , September 2014
On the FOM Algorithm for the Resolution of the Linear Systems Ax = b
Mongi Benhamadou
Show more
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.
Keywords: FOM, Krylov Subspace, Hessenberg Matrix, Sturm Sequence, Givens Method
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.

 
 
Top