On the FOM Algorithm for the Resolution of the Linear Systems Ax = b

Mongi Benhamadou

Department of Mathematics, Faculty of Sciences of Sfax, Sfax, Tunisia.

DOI: 10.4236/alamt.2014.43014                

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

Conflicts of Interest

The authors declare no conflicts of interest.

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