TITLE:
On the FOM Algorithm for the Resolution of the Linear Systems Ax = b
AUTHORS:
Mongi Benhamadou
KEYWORDS:
FOM, Krylov Subspace, Hessenberg Matrix, Sturm Sequence, Givens Method
JOURNAL NAME:
Advances in Linear Algebra & Matrix Theory,
Vol.4 No.3,
September
23,
2014
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.