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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
Résumé: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.
Publications associées à la thèse
Article 1 TH5303:
Titre: Kronecker sum decomposition and its applications
Revue: Annals of Fuzzy Mathematics and Informatics
Référence: Youssouf Mezzar, Kacem Belghaba. Kronecker sum decomposition and its applications, Annals of Fuzzy Mathematics and Informatics, Volume 23 , number 1 , 53-68, 2022.
Date: Février 2022