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On the FOM Algorithm for the Resolution of the Linear Systems Ax = b
Department of Mathematics, Faculty of Sciences of Sfax, Sfax, Tunisia
- 1 Department of Mathematics, Faculty of Sciences of Sfax, Sfax, Tunisia
Advances in Linear Algebra & Matrix Theory·Volume 04 (2014)·Pages 156–171·Published 26 August 2014·DOI10.4236/alamt.2014.43014
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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(n 2 ). 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.
KeywordsFOMKrylov SubspaceHessenberg MatrixSturm SequenceGivens Method
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