Validated numerics: a short introduction to rigorous computations
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
2011
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. [131] - 135. - Index |
| Beschreibung: | XII, 138 S. graph. Darst. |
| ISBN: | 9780691147819 |
Internformat
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| 245 | 1 | 0 | |a Validated numerics |b a short introduction to rigorous computations |c Warwick Tucker |
| 264 | 1 | |a Princeton, NJ |b Princeton University Press |c 2011 | |
| 300 | |a XII, 138 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. [131] - 135. - Index | ||
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Naturwissenschaft | |
| 650 | 4 | |a Numerical calculations |x Verification | |
| 650 | 4 | |a Science |x Data processing | |
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Datensatz im Suchindex
| _version_ | 1804148624026763264 |
|---|---|
| adam_text | Contents
Preface
ix
introduction
xi
What Is Validated Numerics?
xi
The Scope and Aim of This Book
xi
Further Reading
xii
Acknowledgments
xii
Chapter
1.
Computer Arithmetic
1
1.
1 Positional Systems
1
1.2
Floating Point Numbers
2
1.3
Rounding
5
1.4
Floating Point Arithmetic
12
1.5
The IEEE Standard
14
1.6
Examples of Floating Point Computations
19
1.7
Computer Lab I
23
Chapter
2.
Interval Arithmetic
24
2.1
Real Intervals
24
2.2
Real interval Arithmetic
27
2.3
Extended Interval Arithmetic
30
2.4
Floating Point Interval Arithmetic
37
Chapter
3.
Interval Analysis
46
3.1
Interval Functions
46
3.2
Centered Forms
55
3.3
Monotonicity
58
3.4
Computer Lab II
59
Chapter
4.
Automatic Differentiation
60
4Л
First-Order Derivatives
60
4.2
Higher-Order Derivatives
64
4.3
Higher-Order Enclosures
71
4.4
Computer Lab III 72
VIU
CONTENTS
Chapter
5.
Interval Analysis in Action
73
5.1
Zero-Finding Methods
73
5.2
Optimization
87
5.3
Quadrature
94
5.4
Computer Lab IV
105
Chapter
6.
Ordinary Differential Equations
106
6.1
A Gentle Mathematical Introduction
106
6.2
Simple Enclosure Methods
107
6.3
High-Order Methods 111
6.4
Rigorous High-Order Examples
112
Appendix A. Mathematical Foundations
118
A.
1
The Rational Numbers
118
A.2 What Is a Real Number?
120
A.3 Completeness
122
A.4 Fixed-Point Theorems
124
Appendix B. Program Codes
126
B.I IEEE Constants
126
B.2 Changing Rounding Modes
127
B.3 A Sample Code in
C++ 128
Bibliography
131
Index
137
|
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| id | DE-604.BV039738205 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:10:05Z |
| institution | BVB |
| isbn | 9780691147819 |
| language | English |
| lccn | 2010040560 |
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| physical | XII, 138 S. graph. Darst. |
| publishDate | 2011 |
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| spelling | Tucker, Warwick 1970- Verfasser (DE-588)1013541324 aut Validated numerics a short introduction to rigorous computations Warwick Tucker Princeton, NJ Princeton University Press 2011 XII, 138 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. [131] - 135. - Index Datenverarbeitung Naturwissenschaft Numerical calculations Verification Science Data processing Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Intervallalgebra (DE-588)4139152-4 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s Intervallalgebra (DE-588)4139152-4 s DE-604 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024585939&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tucker, Warwick 1970- Validated numerics a short introduction to rigorous computations Datenverarbeitung Naturwissenschaft Numerical calculations Verification Science Data processing Numerische Mathematik (DE-588)4042805-9 gnd Intervallalgebra (DE-588)4139152-4 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4139152-4 |
| title | Validated numerics a short introduction to rigorous computations |
| title_auth | Validated numerics a short introduction to rigorous computations |
| title_exact_search | Validated numerics a short introduction to rigorous computations |
| title_full | Validated numerics a short introduction to rigorous computations Warwick Tucker |
| title_fullStr | Validated numerics a short introduction to rigorous computations Warwick Tucker |
| title_full_unstemmed | Validated numerics a short introduction to rigorous computations Warwick Tucker |
| title_short | Validated numerics |
| title_sort | validated numerics a short introduction to rigorous computations |
| title_sub | a short introduction to rigorous computations |
| topic | Datenverarbeitung Naturwissenschaft Numerical calculations Verification Science Data processing Numerische Mathematik (DE-588)4042805-9 gnd Intervallalgebra (DE-588)4139152-4 gnd |
| topic_facet | Datenverarbeitung Naturwissenschaft Numerical calculations Verification Science Data processing Numerische Mathematik Intervallalgebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024585939&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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