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Interval Analysis : and Automatic Result Verification /
This self-contained text is a step-by-step introduction and a complete overview of interval computation and result verification, a subject whose importance has steadily increased over the past many years. The author, an expert in the field, gently presents the theory of interval analysis through man...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin ; Boston :
De Gruyter,
[2017]
|
| Colección: | De Gruyter studies in mathematics ;
65. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Frontmatter
- Preface
- Contents
- 1. Preliminaries
- 2. Real intervals
- 3. Interval vectors, interval matrices
- 4. Expressions, P-contraction, [epsilon]-inflation
- 5. Linear systems of equations
- 6. Nonlinear systems of equations
- 7. Eigenvalue problems and related ones
- 8. Automatic differentiation
- 9. Complex intervals
- Final Remarks
- Appendix
- A. Proof of the Jordan normal form
- B. Two elementary proofs of Brouwer's fixed point theorem
- C. Proof of the Newton-Kantorovich Theorem
- D. Convergence proof of the row cyclic Jacobi method
- E. The CORDIC algorithm
- F. The symmetric solution set
- a proof of Theorem 5.2.6
- G.A short introduction to INTLAB
- Bibliography
- Symbol Index
- Author Index
- Subject Index.
- Preface ; Contents ; 1 Preliminaries ; 1.1 Notations and basic definitions ; 1.2 Metric spaces ; 1.3 Normed linear spaces ; 1.4 Polynomials ; 1.5 Zeros and fixed points of functions ; 1.6 Mean value theorems ; 1.7 Normal forms of matrices ; 1.8 Eigenvalues.
- 5.4 Direct methods 5.5 Iterative methods ; 6 Nonlinear systems of equations ; 6.1 Newton method
- one-dimensional case ; 6.2 Newton method
- multidimensional case ; 6.3 Krawczyk method ; 6.4 Hansen-Sengupta method ; 6.5 Further existence tests ; 6.6 Bisection method.
- 7 Eigenvalue problems 7.1 Quadratic systems ; 7.2 A Krawczyk-like method ; 7.3 Lohner method ; 7.4 Double or nearly double eigenvalues ; 7.5 The generalized eigenvalue problem ; 7.6 A method due to Behnke ; 7.7 Verification of singular values ; 7.8 An inverse eigenvalue problem.