Matrix Splitting Iteration Method For New Generalized Absolute Value Equations / Ghania Kernani

Public ISBD Titre : Matrix Splitting Iteration Method For New Generalized Absolute Value Equations Type de document : texte imprimé Auteurs : Ghania Kernani, Auteur ; Ikram Rahmani, Auteur ; Merzaka Khaldi, Directeur de thèse Editeur : Sétif:UFA1 Année de publication : 2025 Importance : 1 vol (52 f.) Format : 29 cm Langues : Anglais (eng) Catégories : Thèses & Mémoires:Mathématique Mots-clés : Absolute value equations Linear system Global convergence Picard's iterative methods Newton method Matrix splitting technique Index. décimale : 510-Mathématique Résumé : Abstract: In this dissertation, using the matrix splitting technique, a Newton-based matrix splitting iterative method and a relaxed Newton-based matrix splitting iterative method are established to solve new generalized absolute value equations, which include Picard’s method and the modified Newton-type iteration method. We analyze the sufficient convergence conditions of the proposed methods, with some special coefficient matrices presented. The effectiveness and feasibility of the proposed method are confirmed by some numerical experiments involving both symmetric and non-symmetric matrices. Note de contenu : Contents Introductioniv 1 Mathematicalbackground1 1.1MatrixAnalysis............................1 1.1.1MatrixClasses.........................4 1.2Fixedpointmethod...........................5 1.3Iterativemethodsforsolvingalinearsystems............6 1.3.1Jacobimethod.........................6 1.3.2Gauss-Seidelmethod......................7 1.3.3Relaxationmethod.......................8 1.4Newton-RaphsonÂ’sMethodfornonlinearsystems..........10 1.5Newgeneralizedabsolutevalueequations...............11 1.5.1OnuniquesolvabilityforNGAVE...............11 1.6PicardÂ’siterationmethodforsolvingNGAVE............12 2 MatrixsplittingiterationmethodforNGAVE14 2.1ModiÂ…edNewton-typeiterationmethod................14 2.1.1Convergenceproperty......................17 2.2Newton-basedmatrixsplittingiterationmethod...........20 2.2.1Convergenceproperty......................22 2.3RelaxedNewton-typematrixsplittingiterationmethod.......26 2.3.1Convergenceproperty......................28 2.3.2Generalsu¢cientconvergenceproperty............28 2.3.3Specialsu¢cientconvergencesproperty...........30 3 Numericalresults34 Generalconclusionandperspectives51 Bibliography52 Côte titre : MAM/0773 Matrix Splitting Iteration Method For New Generalized Absolute Value Equations [texte imprimé] / Ghania Kernani, Auteur ; Ikram Rahmani, Auteur ; Merzaka Khaldi, Directeur de thèse . - [S.l.] : Sétif:UFA1, 2025 . - 1 vol (52 f.) ; 29 cm. Langues : Anglais (eng) Catégories : Thèses & Mémoires:Mathématique Mots-clés : Absolute value equations Linear system Global convergence Picard's iterative methods Newton method Matrix splitting technique Index. décimale : 510-Mathématique Résumé : Abstract: In this dissertation, using the matrix splitting technique, a Newton-based matrix splitting iterative method and a relaxed Newton-based matrix splitting iterative method are established to solve new generalized absolute value equations, which include Picard’s method and the modified Newton-type iteration method. We analyze the sufficient convergence conditions of the proposed methods, with some special coefficient matrices presented. The effectiveness and feasibility of the proposed method are confirmed by some numerical experiments involving both symmetric and non-symmetric matrices. Note de contenu : Contents Introductioniv 1 Mathematicalbackground1 1.1MatrixAnalysis............................1 1.1.1MatrixClasses.........................4 1.2Fixedpointmethod...........................5 1.3Iterativemethodsforsolvingalinearsystems............6 1.3.1Jacobimethod.........................6 1.3.2Gauss-Seidelmethod......................7 1.3.3Relaxationmethod.......................8 1.4Newton-RaphsonÂ’sMethodfornonlinearsystems..........10 1.5Newgeneralizedabsolutevalueequations...............11 1.5.1OnuniquesolvabilityforNGAVE...............11 1.6PicardÂ’siterationmethodforsolvingNGAVE............12 2 MatrixsplittingiterationmethodforNGAVE14 2.1ModiÂ…edNewton-typeiterationmethod................14 2.1.1Convergenceproperty......................17 2.2Newton-basedmatrixsplittingiterationmethod...........20 2.2.1Convergenceproperty......................22 2.3RelaxedNewton-typematrixsplittingiterationmethod.......26 2.3.1Convergenceproperty......................28 2.3.2Generalsu¢cientconvergenceproperty............28 2.3.3Specialsu¢cientconvergencesproperty...........30 3 Numericalresults34 Generalconclusionandperspectives51 Bibliography52 Côte titre : MAM/0773

Exemplaires (1)

Code-barres	Cote	Support	Localisation	Section	Disponibilité
MAM/0773	MAM/0773	Mémoire	Bibliothèque des sciences	Anglais	Disponible Disponible

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