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Differential-algebraic systems [[electronic resource] ] : analytical aspects and circuit applications / / Ricardo Riaza
| Differential-algebraic systems [[electronic resource] ] : analytical aspects and circuit applications / / Ricardo Riaza |
| Autore | Riaza Ricardo |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, 2008 |
| Descrizione fisica | 1 online resource (344 p.) |
| Disciplina |
512.56
512/.56 621.3815 |
| Soggetto topico |
Differential-algebraic equations
Electric circuits - Mathematical models |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-93401-1
9786611934019 981-279-181-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. Introduction; 1.1 Historical remarks: Different origins, different names; 1.2 DAE analysis; 1.2.1 Indices; 1.2.2 Dynamics and singularities; 1.2.3 Numerical aspects; 1.3 State vs. semistate modeling; 1.4 Formulations; 1.4.1 Input-output descriptions; 1.4.2 Leading terms; 1.4.3 Semiexplicit, semilinear and quasilinear DAEs; 1.4.3.1 Semiexplicit and semilinear DAEs; 1.4.3.2 Hessenberg DAEs; 1.4.3.3 Quasilinear DAEs; 1.5 Contents and structure of the book; Analytical aspects of DAEs; 2. Linear DAEs and projector-based methods; 2.1 Linear time-invariant DAEs
2.1.1 Matrix pencils and the Kronecker canonical form 2.1.2 Solving linear time-invariant DAEs via the KCF; 2.1.3 A glance at projector-based techniques; 2.1.3.1 Index one characterization via projectors; 2.1.3.2 Decoupling of linear time-invariant index one DAEs; 2.1.3.3 Geometrical remarks; 2.1.3.4 Higher index problems; 2.1.3.5 Some auxiliary properties of the projectors Pi and Qi; 2.2 Properly stated linear time-varying DAEs; 2.2.1 On standard form index one problems; 2.2.2 Properly stated leading terms; 2.2.3 P-projectors: Matrix chain and the tractability index; 2.2.3.1 Matrix chain 2.2.3.2 The tractability index of regular linear DAEs 2.2.4 The Π-framework; 2.2.4.1 Alternative chain construction; 2.2.4.2 Equivalence of the P- and Π-chains; 2.2.4.3 Some properties of the projectors Πi and Mi; 2.2.5 Decoupling; 2.2.6 A tutorial example; 2.2.6.1 Index one; 2.2.6.2 Index two; 2.2.6.3 Index three; 2.2.7 Regular points; 2.3 Standard formlinear DAEs; 2.3.1 The tractability index of standard form DAEs; 2.3.2 Decoupling; 2.3.3 Time-invariant problems revisited; 2.4 Other approaches for linear DAEs: Reduction techniques; 3. Nonlinear DAEs and reduction methods 3.1 Semiexplicit index one DAEs 3.2 Hessenberg systems; 3.3 Some notions from differential geometry; 3.4 Quasilinear DAEs: The geometric index; 3.4.1 The framework of Rabier and Rheinboldt; 3.4.2 Index zero and index one points; 3.4.2.1 Index zero points; 3.4.2.2 Index one points; 3.4.3 Higher index points; 3.4.3.1 Index two points; 3.4.3.2 Index ν points; 3.4.4 Manifold sequences and locally regular DAEs; 3.4.4.1 Regular manifold, solution manifold, and locally regular DAEs; 3.4.4.2 Manifold sequences within different reduction approaches; 3.4.5 Local equivalence 3.4.5.1 The index: Independence of reduction pairs and invariance 3.4.5.2 C-conjugacy of state space descriptions; 3.4.5.3 On the link between local equivalence and reduction operators; 3.4.6 Examples; 3.4.6.1 Semiexplicit index one DAEs; 3.4.6.2 Hessenberg DAEs; 3.4.6.3 A locally regular DAE with di.erent indices; 3.4.7 Nonautonomous problems; 3.4.7.1 Geometric index and reduction in the nonautonomous context; 3.4.7.2 Semiexplicit index one DAEs; 3.4.7.3 Nonautonomous Hessenberg DAEs; 3.4.7.4 Schur reduction and semiexplicit DAEs; 3.5 Dynamical aspects 3.6 Reduction methods for fully nonlinear DAEs |
| Record Nr. | UNINA-9910453278503321 |
Riaza Ricardo
|
||
| Singapore ; ; Hackensack, NJ, : World Scientific, 2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Differential-algebraic systems [[electronic resource] ] : analytical aspects and circuit applications / / Ricardo Riaza
| Differential-algebraic systems [[electronic resource] ] : analytical aspects and circuit applications / / Ricardo Riaza |
| Autore | Riaza Ricardo |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, 2008 |
| Descrizione fisica | 1 online resource (344 p.) |
| Disciplina |
512.56
512/.56 621.3815 |
| Soggetto topico |
Differential-algebraic equations
Electric circuits - Mathematical models |
| ISBN |
1-281-93401-1
9786611934019 981-279-181-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. Introduction; 1.1 Historical remarks: Different origins, different names; 1.2 DAE analysis; 1.2.1 Indices; 1.2.2 Dynamics and singularities; 1.2.3 Numerical aspects; 1.3 State vs. semistate modeling; 1.4 Formulations; 1.4.1 Input-output descriptions; 1.4.2 Leading terms; 1.4.3 Semiexplicit, semilinear and quasilinear DAEs; 1.4.3.1 Semiexplicit and semilinear DAEs; 1.4.3.2 Hessenberg DAEs; 1.4.3.3 Quasilinear DAEs; 1.5 Contents and structure of the book; Analytical aspects of DAEs; 2. Linear DAEs and projector-based methods; 2.1 Linear time-invariant DAEs
2.1.1 Matrix pencils and the Kronecker canonical form 2.1.2 Solving linear time-invariant DAEs via the KCF; 2.1.3 A glance at projector-based techniques; 2.1.3.1 Index one characterization via projectors; 2.1.3.2 Decoupling of linear time-invariant index one DAEs; 2.1.3.3 Geometrical remarks; 2.1.3.4 Higher index problems; 2.1.3.5 Some auxiliary properties of the projectors Pi and Qi; 2.2 Properly stated linear time-varying DAEs; 2.2.1 On standard form index one problems; 2.2.2 Properly stated leading terms; 2.2.3 P-projectors: Matrix chain and the tractability index; 2.2.3.1 Matrix chain 2.2.3.2 The tractability index of regular linear DAEs 2.2.4 The Π-framework; 2.2.4.1 Alternative chain construction; 2.2.4.2 Equivalence of the P- and Π-chains; 2.2.4.3 Some properties of the projectors Πi and Mi; 2.2.5 Decoupling; 2.2.6 A tutorial example; 2.2.6.1 Index one; 2.2.6.2 Index two; 2.2.6.3 Index three; 2.2.7 Regular points; 2.3 Standard formlinear DAEs; 2.3.1 The tractability index of standard form DAEs; 2.3.2 Decoupling; 2.3.3 Time-invariant problems revisited; 2.4 Other approaches for linear DAEs: Reduction techniques; 3. Nonlinear DAEs and reduction methods 3.1 Semiexplicit index one DAEs 3.2 Hessenberg systems; 3.3 Some notions from differential geometry; 3.4 Quasilinear DAEs: The geometric index; 3.4.1 The framework of Rabier and Rheinboldt; 3.4.2 Index zero and index one points; 3.4.2.1 Index zero points; 3.4.2.2 Index one points; 3.4.3 Higher index points; 3.4.3.1 Index two points; 3.4.3.2 Index ν points; 3.4.4 Manifold sequences and locally regular DAEs; 3.4.4.1 Regular manifold, solution manifold, and locally regular DAEs; 3.4.4.2 Manifold sequences within different reduction approaches; 3.4.5 Local equivalence 3.4.5.1 The index: Independence of reduction pairs and invariance 3.4.5.2 C-conjugacy of state space descriptions; 3.4.5.3 On the link between local equivalence and reduction operators; 3.4.6 Examples; 3.4.6.1 Semiexplicit index one DAEs; 3.4.6.2 Hessenberg DAEs; 3.4.6.3 A locally regular DAE with di.erent indices; 3.4.7 Nonautonomous problems; 3.4.7.1 Geometric index and reduction in the nonautonomous context; 3.4.7.2 Semiexplicit index one DAEs; 3.4.7.3 Nonautonomous Hessenberg DAEs; 3.4.7.4 Schur reduction and semiexplicit DAEs; 3.5 Dynamical aspects 3.6 Reduction methods for fully nonlinear DAEs |
| Record Nr. | UNINA-9910782491403321 |
|
Riaza Ricardo
|
||
| Singapore ; ; Hackensack, NJ, : World Scientific, 2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Differential-algebraic systems [[electronic resource] ] : analytical aspects and circuit applications / / Ricardo Riaza
| Differential-algebraic systems [[electronic resource] ] : analytical aspects and circuit applications / / Ricardo Riaza |
| Autore | Riaza Ricardo |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, 2008 |
| Descrizione fisica | 1 online resource (344 p.) |
| Disciplina |
512.56
512/.56 621.3815 |
| Soggetto topico |
Differential-algebraic equations
Electric circuits - Mathematical models |
| ISBN |
1-281-93401-1
9786611934019 981-279-181-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. Introduction; 1.1 Historical remarks: Different origins, different names; 1.2 DAE analysis; 1.2.1 Indices; 1.2.2 Dynamics and singularities; 1.2.3 Numerical aspects; 1.3 State vs. semistate modeling; 1.4 Formulations; 1.4.1 Input-output descriptions; 1.4.2 Leading terms; 1.4.3 Semiexplicit, semilinear and quasilinear DAEs; 1.4.3.1 Semiexplicit and semilinear DAEs; 1.4.3.2 Hessenberg DAEs; 1.4.3.3 Quasilinear DAEs; 1.5 Contents and structure of the book; Analytical aspects of DAEs; 2. Linear DAEs and projector-based methods; 2.1 Linear time-invariant DAEs
2.1.1 Matrix pencils and the Kronecker canonical form 2.1.2 Solving linear time-invariant DAEs via the KCF; 2.1.3 A glance at projector-based techniques; 2.1.3.1 Index one characterization via projectors; 2.1.3.2 Decoupling of linear time-invariant index one DAEs; 2.1.3.3 Geometrical remarks; 2.1.3.4 Higher index problems; 2.1.3.5 Some auxiliary properties of the projectors Pi and Qi; 2.2 Properly stated linear time-varying DAEs; 2.2.1 On standard form index one problems; 2.2.2 Properly stated leading terms; 2.2.3 P-projectors: Matrix chain and the tractability index; 2.2.3.1 Matrix chain 2.2.3.2 The tractability index of regular linear DAEs 2.2.4 The Π-framework; 2.2.4.1 Alternative chain construction; 2.2.4.2 Equivalence of the P- and Π-chains; 2.2.4.3 Some properties of the projectors Πi and Mi; 2.2.5 Decoupling; 2.2.6 A tutorial example; 2.2.6.1 Index one; 2.2.6.2 Index two; 2.2.6.3 Index three; 2.2.7 Regular points; 2.3 Standard formlinear DAEs; 2.3.1 The tractability index of standard form DAEs; 2.3.2 Decoupling; 2.3.3 Time-invariant problems revisited; 2.4 Other approaches for linear DAEs: Reduction techniques; 3. Nonlinear DAEs and reduction methods 3.1 Semiexplicit index one DAEs 3.2 Hessenberg systems; 3.3 Some notions from differential geometry; 3.4 Quasilinear DAEs: The geometric index; 3.4.1 The framework of Rabier and Rheinboldt; 3.4.2 Index zero and index one points; 3.4.2.1 Index zero points; 3.4.2.2 Index one points; 3.4.3 Higher index points; 3.4.3.1 Index two points; 3.4.3.2 Index ν points; 3.4.4 Manifold sequences and locally regular DAEs; 3.4.4.1 Regular manifold, solution manifold, and locally regular DAEs; 3.4.4.2 Manifold sequences within different reduction approaches; 3.4.5 Local equivalence 3.4.5.1 The index: Independence of reduction pairs and invariance 3.4.5.2 C-conjugacy of state space descriptions; 3.4.5.3 On the link between local equivalence and reduction operators; 3.4.6 Examples; 3.4.6.1 Semiexplicit index one DAEs; 3.4.6.2 Hessenberg DAEs; 3.4.6.3 A locally regular DAE with di.erent indices; 3.4.7 Nonautonomous problems; 3.4.7.1 Geometric index and reduction in the nonautonomous context; 3.4.7.2 Semiexplicit index one DAEs; 3.4.7.3 Nonautonomous Hessenberg DAEs; 3.4.7.4 Schur reduction and semiexplicit DAEs; 3.5 Dynamical aspects 3.6 Reduction methods for fully nonlinear DAEs |
| Record Nr. | UNINA-9910828870603321 |
|
Riaza Ricardo
|
||
| Singapore ; ; Hackensack, NJ, : World Scientific, 2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||