| Description |
1 online resource (532 pages) |
| Series |
De Gruyter Studies in Mathematics ; 65 |
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De Gruyter studies in mathematics ; 65.
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| Contents |
880-01 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 |
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880-01/(S Frontmatter -- Preface -- Contents -- 1. Preliminaries -- 2. Real intervals -- 3. Interval vectors, interval matrices -- 4. Expressions, P-contraction, ε-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 |
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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 |
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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 |
| Summary |
880-02 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 many examples and exercises, and guides the reader from the basics of the theory to current research topics in the mathematics of computation. Contents Preliminaries Real intervals Interval vectors, interval matrices Expressions, P-contraction, [epsilon]-inflation Linear systems of equations Nonlinear systems of equations Eigenvalue problems Automatic differentiation Complex intervals |
|
880-02/(S 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 many examples and exercises, and guides the reader from the basics of the theory to current research topics in the mathematics of computation. Contents Preliminaries Real intervals Interval vectors, interval matrices Expressions, P-contraction, ε-inflation Linear systems of equations Nonlinear systems of equations Eigenvalue problems Automatic differentiation Complex intervals |
|
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer |
| Analysis |
(Produktform)Electronic book text |
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(Zielgruppe)Fachpublikum/ Wissenschaft |
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(BISAC Subject Heading)MAT041000 |
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(BISAC Subject Heading)MAT034000: MAT034000 MATHEMATICS / Mathematical Analysis |
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(BISAC Subject Heading)MAT005000: MAT005000 MATHEMATICS / Calculus |
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(BISAC Subject Heading)COM051300: COM051300 COMPUTERS / Programming / Algorithms |
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Computerarithmetik |
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Automatische Differentiation |
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Intervalanalyse |
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Intervalalgebra |
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Richrigkeit von Ergebnissen |
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(VLB-WN)9620 |
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(Produktrabattgruppe)PR: rabattbeschränkt/Bibliothekswerke |
| Bibliography |
Includes bibliographical references (pages 483-498) and indexes |
| Notes |
In English |
|
Online resource; title from PDF title page (publisher's Web site, viewed Apr. 18, 2017) |
| Subject |
Interval analysis (Mathematics)
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MATHEMATICS -- Numerical Analysis.
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Interval analysis (Mathematics)
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Calcul sur des intervalles.
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| Form |
Electronic book
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| LC no. |
2017288658 |
| ISBN |
9783110499469 |
|
3110499460 |
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9783110498059 |
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3110498057 |
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9783110500639 |
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3110500639 |
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9783110499476 |
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3110499479 |
|
