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Matrix computations and semiseparable matrices. V.2. Eigenvalue and singular value methods /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Baltimore :
Johns Hopkins University Press,
2008-
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- ""Contents""; ""Preface""; ""Notation""; ""1 Introduction to semiseparable matrices""; ""1.1 Definition of semiseparable matrices""; ""1.2 Some properties""; ""1.2.1 Relations under inversion""; ""1.2.2 Generator representable semiseparable matrices""; ""1.3 The representations""; ""1.3.1 The generator representation""; ""1.3.2 The Givens-vector representation""; ""1.4 Conclusions""; ""I: The reduction of matrices""; ""2 Algorithms for reducing matrices""; ""2.1 Introduction""; ""2.2 Orthogonal similarity transformations of symmetric matrices""
- ""2.3 Orthogonal similarity transformation of (unsymmetric) matrices""""2.4 Orthogonal transformations of matrices""; ""2.5 Transformations from sparse to structured rank form""; ""2.6 From structured rank to sparse form""; ""2.7 Conclusions""; ""3 Convergence properties of the reduction algorithms""; ""3.1 The Arnoldi(Lanczos)-Ritz values""; ""3.2 Subspace iteration inside the reduction algorithms""; ""3.3 Interaction of the convergence behaviors""; ""3.4 Conclusions""; ""4 Implementation of the algorithms and numerical experiments""; ""4.1 Working with Givens transformations""
- ""4.2 Implementation details""""4.3 Numerical experiments""; ""4.4 Conclusions""; ""II: QR-algorithms (eigenvalue problems)""; ""5 Introduction: traditional sparse QR-algorithms""; ""5.1 On the QR-algorithm""; ""5.2 A QR-algorithm for sparse matrices""; ""5.3 An implicit QR-method for sparse matrices""; ""5.4 On computing the singular values""; ""5.5 Conclusions""; ""6 Theoretical results for structured rank QR-algorithms""; ""6.1 Preserving the structure under a QR-step""; ""6.2 An implicit Q-theorem""; ""6.3 On Hessenberg-like plus diagonal matrices""; ""6.4 Conclusions""
- ""7 Implicit QR-methods for semiseparable matrices""""7.1 An implicit QR-algorithm for symmetric semiseparable matrices""; ""7.2 A QR-algorithm for semiseparable plus diagonal""; ""7.3 An implicit QR-algorithm for Hessenberg-like matrices""; ""7.4 An implicit QR-algorithm for computing the singular values""; ""7.5 Conclusions""; ""8 Implementation and numerical experiments""; ""8.1 Working with Givens transformations""; ""8.2 Implementation of the QR-algorithm for semiseparable matrices""; ""8.3 Computing the eigenvectors""; ""8.4 Numerical experiments""; ""8.5 Conclusions""
- ""9 More on QR-related algorithms""""9.1 Complex arithmetic and Givens transformations""; ""9.2 Variations of the QR-algorithm""; ""9.3 The QR-method for quasiseparable matrices""; ""9.4 The multishift QR-algorithm""; ""9.5 A QH-algorithm""; ""9.6 Computing zeros of polynomials""; ""9.7 References to related subjects""; ""9.8 Conclusions""; ""III: Some generalizations and miscellaneous topics""; ""10 Divide-and-conquer algorithms for the eigendecomposition""; ""10.1 Arrowhead and diagonal plus rank 1 matrices""; ""10.2 Divide-and-conquer algorithms for tridiagonal matrices""