Matrix splitting iteration method for generalized absolute value matrix equation / Amel Chouadra  

Public ISBD Titre : Matrix splitting iteration method for generalized absolute value matrix equation Type de document : document électronique Auteurs : Amel Chouadra, Auteur ; Israa Alioui, Auteur ; Merzaka Khaldi, Directeur de thèse Editeur : Sétif:UFS Année de publication : 2025 Importance : 1 vol (66 f.) Format : 29 cm Langues : Anglais (eng) Mots-clés : Generalized absolute value equations Matrix splitting Newton methods Picard method Global convergence Iterative methods Résumé : In this dissertation, we study generalized absolute value matrix equations of the form AX−B|X|=C where A, B, C, X ∈ R^(n×n) ,which are non linear due to the presence of the absolute value operator. Using the matrix splitting technique, we propose a Newton-based iterative method as well as a relaxeds versions. This general framework includes classical methods such as Picard’s method and the modified Newton method. We establish sufficient conditions and analyze the convergence properties, proving global linear convergence under suitable assumptions. Numerical experiments carried out using MATLAB confirm the effectiveness of the proposed methods for both symmetric and non-symmetric matrices. Note de contenu : Contents Table of Contents 5 1. Mathematical background 13 1.1 Matrix Analysis . . . . ……………. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 13 1.1.1 Matrix Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 17 1.2 Fixed point method . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 18 1.3 Iterative methods for solving a linear system . . . . . . . . . . . . . . . . . . . . . . . . 19 1.3.1 Jacobi method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ………………. 19 1.3.2 Gauss-Seidel method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . …………20 1.4 Newton-Raphson’s method for non linear systems . . . . . . . . . . . . . . . . . . . 21 2. Matrix splitting iteration method for GAVME 23 2.1 Generalization absulte value matrix equations (GAVME) . . . . . . . … .. . . . 23 2.2 On unique solvability for GAVME . . . . . . . . . . . . . . . . . . . . . . . . . …….. . 24 2.3 Picard’s Iterative method for GAVME . . . ….... . . . . . . . . . . . . . . . . . . . . . 25 2.3.1 Convergence analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.4 Modified Newton-type iteration method for GAVME . . . . . . . . . . . . . . . . . 27 2.4.1 Convergence analysis. . . ………….... . . . . . . . . . . . . . . . . .. . . . . . . . . 28 2.5 Newton-based matrix splitting iterative method . … . . . . . . . . . . . . . . . . . . 31 2.5.1 Convergence analysis. . . . ………….... . . . . . . . . . . . 34 3. Numerical results 40 Bibliography 66 Côte titre : MAM/0843 En ligne : https://repository.univ-setif.dz/server/api/core/bitstreams/e4482b70-47d9-49c3-9 [...] Matrix splitting iteration method for generalized absolute value matrix equation [document électronique] / Amel Chouadra, Auteur ; Israa Alioui, Auteur ; Merzaka Khaldi, Directeur de thèse . - [S.l.] : Sétif:UFS, 2025 . - 1 vol (66 f.) ; 29 cm. Langues : Anglais (eng) Mots-clés : Generalized absolute value equations Matrix splitting Newton methods Picard method Global convergence Iterative methods Résumé : In this dissertation, we study generalized absolute value matrix equations of the form AX−B|X|=C where A, B, C, X ∈ R^(n×n) ,which are non linear due to the presence of the absolute value operator. Using the matrix splitting technique, we propose a Newton-based iterative method as well as a relaxeds versions. This general framework includes classical methods such as Picard’s method and the modified Newton method. We establish sufficient conditions and analyze the convergence properties, proving global linear convergence under suitable assumptions. Numerical experiments carried out using MATLAB confirm the effectiveness of the proposed methods for both symmetric and non-symmetric matrices. Note de contenu : Contents Table of Contents 5 1. Mathematical background 13 1.1 Matrix Analysis . . . . ……………. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 13 1.1.1 Matrix Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 17 1.2 Fixed point method . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 18 1.3 Iterative methods for solving a linear system . . . . . . . . . . . . . . . . . . . . . . . . 19 1.3.1 Jacobi method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ………………. 19 1.3.2 Gauss-Seidel method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . …………20 1.4 Newton-Raphson’s method for non linear systems . . . . . . . . . . . . . . . . . . . 21 2. Matrix splitting iteration method for GAVME 23 2.1 Generalization absulte value matrix equations (GAVME) . . . . . . . … .. . . . 23 2.2 On unique solvability for GAVME . . . . . . . . . . . . . . . . . . . . . . . . . …….. . 24 2.3 Picard’s Iterative method for GAVME . . . ….... . . . . . . . . . . . . . . . . . . . . . 25 2.3.1 Convergence analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.4 Modified Newton-type iteration method for GAVME . . . . . . . . . . . . . . . . . 27 2.4.1 Convergence analysis. . . ………….... . . . . . . . . . . . . . . . . .. . . . . . . . . 28 2.5 Newton-based matrix splitting iterative method . … . . . . . . . . . . . . . . . . . . 31 2.5.1 Convergence analysis. . . . ………….... . . . . . . . . . . . 34 3. Numerical results 40 Bibliography 66 Côte titre : MAM/0843 En ligne : https://repository.univ-setif.dz/server/api/core/bitstreams/e4482b70-47d9-49c3-9 [...]

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Code-barres	Cote	Support	Localisation	Section	Disponibilité
MAM/0843	MAM/0843	Mémoire	Bibliothèque des sciences	Anglais	Disponible Disponible

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