Titre :	The generalized Newton method for the absolute value matrix equation
Type de document :	texte imprimé
Auteurs :	Imene Boulharts, Auteur ; Chourouk Arama ; Nassima Anane, Directeur de thèse
Editeur :	Sétif:UFS
Année de publication :	2024
Importance :	1 vol (45 f.)
Format :	29 cm
Langues :	Anglais (eng)
Catégories :	Thèses & Mémoires:Mathématique
Mots-clés :	Absolute value matrix equations linear system Singular value Picard's iterative method Generalized Newton method
Index. décimale :	510-Mathématique
Résumé :	In this dissertation, we have investigated a class of the generalized absolute value matrix equations (GAVME) A????−????|????|=????,(????, ????,????,????∈ℝ????×????). We have also derived weaker sufficient conditions for the unique solvability of the (GAVME). Picard's iterative method and a generalized Newton method are proposed for its numerical solution. Furthermore, we have demonstrated, under suitable assumptions, the well-definedness of the proposed algorithms and their global linear convergence to the unique solution of the (GAVME). Finally, we present a diverse set of numerical results to illustrate the efficiency of our proposed approaches.
Note de contenu :	Sommaire Introductionv 1 Mathematicalbackground1 1.1Matrixanalysis.............................1 1.2Di¤erentialcalculus...........................4 1.3Convexanalysis.............................6 1.3.1Convexfunction.........................6 1.3.2Stronglyconvexfunction....................7 1.3.3GeneralizedJacobianinthesenseofClarke.........7 1.4Absolutevaluematrixequation....................8 1.4.1ThestandardLinearComplementarityProblem.......8 1.4.2ThehorizontalLinearComplementarityProblem......9 1.5Someresultsoftheexistenceanduniquenessofthesolutionofthe GAVEandGAVME..........................10 1.6AgeneralizedNewtonmethod....................16 1.7Fixedpoint(Picard)method......................17 2 Numericalsolutionofabsolutevaluematrixequations18 2.1OnuniquesolvabilityforGAVME...................18 2.2AgeneralizedNewtonmethodforGAVME..............19 2.2.1Algorithm............................21 2.2.2Convergenceresults.......................21 2.3Picard’siterativemethodforGAVME................24 2.3.1Algorithm............................26 2.3.2Convergencestudy.......................26 3 Numericalexperiments28 3.1Examples................................28 4 Generalconclusionandperspective 41
Côte titre :	MAM/0714

The generalized Newton method for the absolute value matrix equation [texte imprimé] / Imene Boulharts, Auteur ; Chourouk Arama ; Nassima Anane, Directeur de thèse . - [S.l.] : Sétif:UFS, 2024 . - 1 vol (45 f.) ; 29 cm.
Langues : Anglais (eng)

Catégories :	Thèses & Mémoires:Mathématique
Mots-clés :	Absolute value matrix equations linear system Singular value Picard's iterative method Generalized Newton method
Index. décimale :	510-Mathématique
Résumé :	In this dissertation, we have investigated a class of the generalized absolute value matrix equations (GAVME) A????−????|????|=????,(????, ????,????,????∈ℝ????×????). We have also derived weaker sufficient conditions for the unique solvability of the (GAVME). Picard's iterative method and a generalized Newton method are proposed for its numerical solution. Furthermore, we have demonstrated, under suitable assumptions, the well-definedness of the proposed algorithms and their global linear convergence to the unique solution of the (GAVME). Finally, we present a diverse set of numerical results to illustrate the efficiency of our proposed approaches.
Note de contenu :	Sommaire Introductionv 1 Mathematicalbackground1 1.1Matrixanalysis.............................1 1.2Di¤erentialcalculus...........................4 1.3Convexanalysis.............................6 1.3.1Convexfunction.........................6 1.3.2Stronglyconvexfunction....................7 1.3.3GeneralizedJacobianinthesenseofClarke.........7 1.4Absolutevaluematrixequation....................8 1.4.1ThestandardLinearComplementarityProblem.......8 1.4.2ThehorizontalLinearComplementarityProblem......9 1.5Someresultsoftheexistenceanduniquenessofthesolutionofthe GAVEandGAVME..........................10 1.6AgeneralizedNewtonmethod....................16 1.7Fixedpoint(Picard)method......................17 2 Numericalsolutionofabsolutevaluematrixequations18 2.1OnuniquesolvabilityforGAVME...................18 2.2AgeneralizedNewtonmethodforGAVME..............19 2.2.1Algorithm............................21 2.2.2Convergenceresults.......................21 2.3Picard’siterativemethodforGAVME................24 2.3.1Algorithm............................26 2.3.2Convergencestudy.......................26 3 Numericalexperiments28 3.1Examples................................28 4 Generalconclusionandperspective 41
Côte titre :	MAM/0714