Introduction to interval analysis:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia, PA
Society for Industrial and Applied Mathematics
2009
|
| Subjects: | |
| Online Access: | Klappentext Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 201-218) and index |
| Physical Description: | XI, 223 S. graph. Darst. |
| ISBN: | 9780898716696 0898716691 |
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MARC
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| 245 | 1 | 0 | |a Introduction to interval analysis |c Ramon E. Moore, R. Baker Kearfott, Michael J. Cloud |
| 264 | 1 | |a Philadelphia, PA |b Society for Industrial and Applied Mathematics |c 2009 | |
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Record in the Search Index
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This unique book is an introduction to a subject whose use has steadily increased over the past
40
years. An update of Ramon Moore's previous books on the topic, it provides broad coverage of the
subject as well as the historical perspective of one of the originators of modern interval analysis.
The authors give a hands-on introduction to INTLAB, a high-quality, comprehensive
MATLAB®
toolbox for interval computations, making this the first interval analysis book that does with
INTLAB what general numerical analysis texts do with
MATLAB.
Readers will find the following features of interest:
•
Elementary motivating examples and notes.
•
Exercises and hands-on MATLAB-based examples woven into the text.
•
INTLAB-based examples and explanations integrated into the text, a comprehensive set
of exercises and solutions, and an appendix with INTLAB commands.
•
An extensive bibliography and appendices that will continue to be valuable resources once
the reader is familiar with the subject.
•
A Web page with links to computational tools and other resources of interest.
Introduction to Interval Analysis will be valuable to engineers and scientists interested in scientific
computation, especially in reliability, effects of roundoff error, and automatic verification of results.
The introductory material is particulaKy important for experts in global optimization and constraint
solution algorithms. This book is suitable for introducing the subject to students in these areas.
Raum·
E.
Moore authored Interval Analysis (Prentice-Hall,
1966),
Methods and Applications
of Interval Analysis (SIAM,
1979),
and numerous related publications. Now retired, he was professor
of computer science and/or mathematics from
1965
through
2000
at universities in Ohio, Texas,
and Wisconsin as well as visiting professor in Stockholm, Oxford, Karlsruhe, and Freiburg. From
1950
until
1965
he worked in the area of computational mathematics at Aberdeen Proving Grounds, UC
Radiation Lab in Livermore, and Lockheed Research Labs in Palo Alto. He received an Alexander
von
Humboldt
Foundation-US Senior Scientist Award in
1975.
R. laker Kearfott has authored a monograph on mathematically rigorous numerical methods for
nonlinear algebraic systems of equations and nonlinear optimization problems, organized a major
international conference on interval computations, edited several conference volumes, and provided
several software packages for interval computations. He has been on the faculty of the University
of Louisiana at Lafayette since
1977
and has participated in various modeling projects at the
University of Louisiana and while at Exxon Research and Engineering.
Mkh—t
3.
Cloud has been a faculty member in the Department of Electrical and Computer
Engineering at Lawrence Technological University since
1987
and currently holds the rank
of Associate Professor. He has coauthored seven other books.
For more information about SIAM books, journals,
conferences, memberships, or activities, contact:
Society for Industrial and Applied Mathematics
3600
Market Street, 6th Floor
Philadelphia, PA
19104-2688
USA
+1-215-382-9800 ·
Fax
+1-215-386-7999
siam@siam.org
·
www.siam.org
Titel: Introduction to interval analysis
Autor: Moore, Ramon E.
Jahr: 2009
Contents
Preface ix
1 Introduction 1
1.1 Enclosing a Solution. 1
1.2 Bounding Roundoff Error. 3
1.3 Number Pair Extensions. 5
2 The Interval Number System 7
2.1 Basic Terms and Concepts. 7
2.2 Order Relations for Intervals . 9
2.3 Operations of Interval Arithmetic. 10
2.4 Interval Vectors and Matrices. 14
2.5 Some Historical References. 16
3 First Applications of Interval Arithmetic 19
3.1 Examples. 19
3.2 Outwardly Rounded Interval Arithmetic. 22
3.3 INTLAB. 22
3.4 Other Systems and Considerations. 28
4 Further Properties of Interval Arithmetic 31
4.1 Algebraic Properties. 31
4.2 Symmetric Intervals. 33
4.3 Inclusion Isotonicity of Interval Arithmetic. 34
5 Introduction to Interval Functions 37
5.1 Set Images and United Extension. 37
5.2 Elementary Functions of Interval Arguments. 38
5.3 Interval-Valued Extensions of Real Functions. 42
5.4 The Fundamental Theorem and Its Applications. 45
5.5 Remarks on Numerical Computation. 49
6 Interval Sequences 51
6.1 A Metric for the Set of Intervals. 51
6.2 Refinement. 53
6.3 Finite Convergence and Stopping Criteria.57
6.4 More Efficient Refinements.64
6.5 Summary.83
7 Interval Matrices 85
7.1 Definitions. 85
7.2 Interval Matrices and Dependency . 86
7.3 INTLAB Support for Matrix Operations. 87
7.4 Systems of Linear Equations . 88
7.5 Linear Systems with Inexact Data. 92
7.6 More on Gaussian Elimination. 100
7.7 Sparse Linear Systems Within INTLAB . 101
7.8 Final Notes. 103
8 Interval Newton Methods 105
8.1 Newton's Method in One Dimension.105
8.2 The Krawczyk Method .116
8.3 Safe Starting Intervals.121
8.4 Multivariate Interval Newton Methods.123
8.5 Concluding Remarks .127
9 Integration of Interval Functions 129
9.1 Definition and Properties of the Integral. 129
9.2 Integration of Polynomials .133
9.3 Polynomial Enclosure, Automatic Differentiation .135
9.4 Computing Enclosures for Integrals.141
9.5 Further Remarks on Interval Integration .145
9.6 Software and Further References.147
10 Integral and Differential Equations 149
10.1 Integral Equations.149
10.2 ODEs and Initial Value Problems.151
10.3 ODEs and Boundary Value Problems.156
10.4 Partial Differential Equations.156
11 Applications 157
11.1 Computer-Assisted Proofs. 157
11.2 Global Optimization and Constraint Satisfaction. 159
11.2.1 A Prototypical Algorithm. 159
11.2.2 Parameter Estimation. 161
11.2.3 Robotics Applications. 162
11.2.4 Chemical Engineering Applications. 163
11.2.5 Water Distribution Network Design. 164
11.2.6 Pitfalls and Clarifications. 164
11.2.7 Additional Centers of Study. 167
11.2.8 Summary of Links for Further Study. 168
11.3 Structural Engineering Applications. 168
11.4 Computer Graphics. 169
11.5 Computation of Physical Constants. 169
11.6 Other Applications. 170
11.7 For Further Study. 170
A Sets and Functions 171
B Formulary 177
C Hints for Selected Exercises 185
D Internet Resources 195
E INTLAB Commands and Functions 197
References 201
Index 219 |
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| discipline | Mathematik |
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| spelling | Moore, Ramon E. 1929-2015 Verfasser (DE-588)108802817 aut Introduction to interval analysis Ramon E. Moore, R. Baker Kearfott, Michael J. Cloud Philadelphia, PA Society for Industrial and Applied Mathematics 2009 XI, 223 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. 201-218) and index Analyse numérique ram Calcul d'erreur ram Calcul sur des intervalles ram Interval analysis (Mathematics) Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Intervallmathematik (DE-588)4130580-2 gnd rswk-swf Intervallanalyse (DE-588)4162150-5 gnd rswk-swf Intervallanalyse (DE-588)4162150-5 s DE-604 Intervallmathematik (DE-588)4130580-2 s Numerische Mathematik (DE-588)4042805-9 s 1\p DE-604 Kearfott, Ralph Baker Verfasser (DE-588)138320861 aut Cloud, Michael J. 1960- Verfasser (DE-588)120264242 aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017727052&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Klappentext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017727052&sequence=000006&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Moore, Ramon E. 1929-2015 Kearfott, Ralph Baker Cloud, Michael J. 1960- Introduction to interval analysis Analyse numérique ram Calcul d'erreur ram Calcul sur des intervalles ram Interval analysis (Mathematics) Numerische Mathematik (DE-588)4042805-9 gnd Intervallmathematik (DE-588)4130580-2 gnd Intervallanalyse (DE-588)4162150-5 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4130580-2 (DE-588)4162150-5 |
| title | Introduction to interval analysis |
| title_auth | Introduction to interval analysis |
| title_exact_search | Introduction to interval analysis |
| title_full | Introduction to interval analysis Ramon E. Moore, R. Baker Kearfott, Michael J. Cloud |
| title_fullStr | Introduction to interval analysis Ramon E. Moore, R. Baker Kearfott, Michael J. Cloud |
| title_full_unstemmed | Introduction to interval analysis Ramon E. Moore, R. Baker Kearfott, Michael J. Cloud |
| title_short | Introduction to interval analysis |
| title_sort | introduction to interval analysis |
| topic | Analyse numérique ram Calcul d'erreur ram Calcul sur des intervalles ram Interval analysis (Mathematics) Numerische Mathematik (DE-588)4042805-9 gnd Intervallmathematik (DE-588)4130580-2 gnd Intervallanalyse (DE-588)4162150-5 gnd |
| topic_facet | Analyse numérique Calcul d'erreur Calcul sur des intervalles Interval analysis (Mathematics) Numerische Mathematik Intervallmathematik Intervallanalyse |
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