University Sétif 1 FERHAT ABBAS Faculty of Sciences
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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 methodIndex. 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
2.3PicardsiterativemethodforGAVME................24
2.3.1Algorithm............................26
2.3.2Convergencestudy.......................26
3 Numericalexperiments28
3.1Examples................................28
4 Generalconclusionandperspective 41Côte 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 methodIndex. 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
2.3PicardsiterativemethodforGAVME................24
2.3.1Algorithm............................26
2.3.2Convergencestudy.......................26
3 Numericalexperiments28
3.1Examples................................28
4 Generalconclusionandperspective 41Côte titre : MAM/0714 Exemplaires
Code-barres Cote Support Localisation Section Disponibilité aucun exemplaire
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 methodIndex. 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
2.3PicardsiterativemethodforGAVME................24
2.3.1Algorithm............................26
2.3.2Convergencestudy.......................26
3 Numericalexperiments28
3.1Examples................................28
4 Generalconclusionandperspective 41Côte 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 methodIndex. 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
2.3PicardsiterativemethodforGAVME................24
2.3.1Algorithm............................26
2.3.2Convergencestudy.......................26
3 Numericalexperiments28
3.1Examples................................28
4 Generalconclusionandperspective 41Côte titre : MAM/0714 Exemplaires
Code-barres Cote Support Localisation Section Disponibilité aucun exemplaire
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 methodIndex. 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
2.3PicardsiterativemethodforGAVME................24
2.3.1Algorithm............................26
2.3.2Convergencestudy.......................26
3 Numericalexperiments28
3.1Examples................................28
4 Generalconclusionandperspective 41Côte 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 methodIndex. 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
2.3PicardsiterativemethodforGAVME................24
2.3.1Algorithm............................26
2.3.2Convergencestudy.......................26
3 Numericalexperiments28
3.1Examples................................28
4 Generalconclusionandperspective 41Côte titre : MAM/0714 Exemplaires (1)
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