Details
| Title | De Gruyter studies in mathematics ;. — Interval Analysis. — v. 65. – 2017. |
|---|---|
| Creators | Mayer Günter. |
| Imprint | Berlin/Boston: De Gruyter, 2017 |
| Collection | Электронные книги зарубежных издательств ; Общая коллекция |
| Subjects | Interval analysis (Mathematics) ; MATHEMATICS / Applied ; MATHEMATICS / Probability & Statistics / General ; EBSCO eBooks |
| Document type | Other |
| File type | |
| Language | English |
| Rights | Доступ по паролю из сети Интернет (чтение, печать, копирование) |
| Record key | ocn985959592 |
| Record create date | 5/5/2017 |
Allowed Actions
| pdf/1504932.pdf | – |
Action 'Read' will be available if you login or access site from another network
Action 'Download' will be available if you login or access site from another network
|
|---|---|---|
| epub/1504932.epub | – |
Action 'Download' will be available if you login or access site from another network
|
| Group | Anonymous |
|---|---|
| Network | Internet |
| Network | User group | Action |
|---|---|---|
| ILC SPbPU Local Network | All |
|
| Internet | Authorized users SPbPU |
|
| Internet | Anonymous |
|
- 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
- 1.9 Nonnegative matrices
- 1.10 Particular matrices
- 2 Real intervals
- 2.1 Intervals, partial ordering
- 2.2 Interval arithmetic
- 2.3 Algebraic properties, χ -function
- 2.4 Auxiliary functions
- 2.5 Distance and topology
- 2.6 Elementary interval functions
- 2.7 Machine interval arithmetic
- 3 Interval vectors, interval matrices
- 3.1 Basics
- 3.2 Powers of interval matrices
- 3.3 Particular interval matrices
- 4 Expressions, P-contraction, ε-inflation
- 4.1 Expressions, range
- 4.2 P-contraction
- 4.3 ε-inflation
- 5 Linear systems of equations
- 5.1 Motivation
- 5.2 Solution sets
- 5.3 Interval hull
- 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
- 8 Automatic differentiation
- 8.1 Forward mode
- 8.2 Backward mode
- 9 Complex intervals
- 9.1 Rectangular complex intervals
- 9.2 Circular complex intervals
- 9.3 Applications of complex intervals
- Final Remarks
- Appendix
- A Jordan normal form
- B Brouwer’s fixed point theorem
- C Theorem of Newton–Kantorovich
- D The row cyclic Jacobi method
- E The CORDIC Algorithm
- F The symmetric solution set
- G INTLAB
- Bibliography
- Symbol Index
- Author Index
- Subject Index
