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Titre: On some nonstationary iterative methods for large linear systems.

Domaine: Mathématiques informatique (MI)

Filière: Mathématique

Option: MATHEMATIQUES ET APPLICATIONS.

Auteur: MEZZAR Youssouf

Soutenu (e) le: 03/02/2022

Sous la direction de: BELGHABA Kacem, Professeur, Université Oran 1

Le président du jury : SMAIL Abderrahmane, Professeur, Université Oran 1

Examinateur1: TIMIMOUN Chahnaz Zakia, MCA, Université Oran 1

Examinateur2: BOUDAOUD Fatima, Professeur, Université Oran 1

Examinateur3: OULD ALI Mohand, Professeur, Université Mostaganem

Examinateur4: BENAISSA Abbes, Professeur, Université Djilali Liabes

Invité: ELARBI BENATTIA Mohamed, MCA, E.S.E Mostaganem

Mention: Très honorables

In this work, we studied iterative methods and their importance in solving systems of linear equations and convergence velocity, in particular, nonstationary iterative methods for large linear systems include conjugated gradient method, Generalized Conjugate Residual method, and Generalized Minimum RESidual method. And we preconditioned and adapted it to solve matrix equations by developing a new matrix decomposition that we called " Kronecker Sum Decomposition "

Mots clefs: Linear System; Iterative Methods; Convergence; Krylov Methods; Matrix Equation; Nonstationary Iterative Methods; Kronecker Product; Kronecker Sum; Kronecker Sum Decomposition; Preconditioner.

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