Validated Numerics: A Short Introduction to Rigorous Computations
This textbook provides a comprehensive introduction to the theory and practice of validated numerics, an emerging new field that combines the strengths of scientific computing and pure mathematics. In numerous fields ranging from pharmaceutics and engineering to weather prediction and robotics, fast...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
[2011]
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This textbook provides a comprehensive introduction to the theory and practice of validated numerics, an emerging new field that combines the strengths of scientific computing and pure mathematics. In numerous fields ranging from pharmaceutics and engineering to weather prediction and robotics, fast and precise computations are essential. Based on the theory of set-valued analysis, a new suite of numerical methods is developed, producing efficient and reliable solvers for numerous problems in nonlinear analysis. Validated numerics yields rigorous computations that can find all possible solutions to a problem while taking into account all possible sources of error--fast, and with guaranteed accuracy. Validated Numerics offers a self-contained primer on the subject, guiding readers from the basics to more advanced concepts and techniques. This book is an essential resource for those entering this fast-developing field, and it is also the ideal textbook for graduate students and advanced undergraduates needing an accessible introduction to the subject. Validated Numerics features many examples, exercises, and computer labs using MATLAB/C++, as well as detailed appendixes and an extensive bibliography for further reading. Provides a comprehensive, self-contained introduction to validated numerics Requires no advanced mathematics or programming skills Features many examples, exercises, and computer labs Includes code snippets that illustrate implementation Suitable as a textbook for graduate students and advanced undergraduates |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed 26. Nov 2019) |
| Beschreibung: | 1 online resource (152 pages) 41 line illus. 12 tables |
| ISBN: | 9781400838974 |
| DOI: | 10.1515/9781400838974 |
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| 520 | |a This textbook provides a comprehensive introduction to the theory and practice of validated numerics, an emerging new field that combines the strengths of scientific computing and pure mathematics. In numerous fields ranging from pharmaceutics and engineering to weather prediction and robotics, fast and precise computations are essential. Based on the theory of set-valued analysis, a new suite of numerical methods is developed, producing efficient and reliable solvers for numerous problems in nonlinear analysis. Validated numerics yields rigorous computations that can find all possible solutions to a problem while taking into account all possible sources of error--fast, and with guaranteed accuracy. Validated Numerics offers a self-contained primer on the subject, guiding readers from the basics to more advanced concepts and techniques. This book is an essential resource for those entering this fast-developing field, and it is also the ideal textbook for graduate students and advanced undergraduates needing an accessible introduction to the subject. Validated Numerics features many examples, exercises, and computer labs using MATLAB/C++, as well as detailed appendixes and an extensive bibliography for further reading. Provides a comprehensive, self-contained introduction to validated numerics Requires no advanced mathematics or programming skills Features many examples, exercises, and computer labs Includes code snippets that illustrate implementation Suitable as a textbook for graduate students and advanced undergraduates | ||
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| discipline | Allgemeine Naturwissenschaft |
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| id | DE-604.BV046285690 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:40:35Z |
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| isbn | 9781400838974 |
| language | English |
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| spelling | Tucker, Warwick aut Validated Numerics A Short Introduction to Rigorous Computations Warwick Tucker Princeton, NJ Princeton University Press [2011] © 2011 1 online resource (152 pages) 41 line illus. 12 tables txt rdacontent c rdamedia cr rdacarrier Description based on online resource; title from PDF title page (publisher's Web site, viewed 26. Nov 2019) This textbook provides a comprehensive introduction to the theory and practice of validated numerics, an emerging new field that combines the strengths of scientific computing and pure mathematics. In numerous fields ranging from pharmaceutics and engineering to weather prediction and robotics, fast and precise computations are essential. Based on the theory of set-valued analysis, a new suite of numerical methods is developed, producing efficient and reliable solvers for numerous problems in nonlinear analysis. Validated numerics yields rigorous computations that can find all possible solutions to a problem while taking into account all possible sources of error--fast, and with guaranteed accuracy. Validated Numerics offers a self-contained primer on the subject, guiding readers from the basics to more advanced concepts and techniques. This book is an essential resource for those entering this fast-developing field, and it is also the ideal textbook for graduate students and advanced undergraduates needing an accessible introduction to the subject. Validated Numerics features many examples, exercises, and computer labs using MATLAB/C++, as well as detailed appendixes and an extensive bibliography for further reading. Provides a comprehensive, self-contained introduction to validated numerics Requires no advanced mathematics or programming skills Features many examples, exercises, and computer labs Includes code snippets that illustrate implementation Suitable as a textbook for graduate students and advanced undergraduates In English MATHEMATICS / Applied bisacsh 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 1\p DE-604 https://doi.org/10.1515/9781400838974 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Tucker, Warwick Validated Numerics A Short Introduction to Rigorous Computations MATHEMATICS / Applied bisacsh 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 | MATHEMATICS / Applied bisacsh Numerical calculations Verification Science Data processing Numerische Mathematik (DE-588)4042805-9 gnd Intervallalgebra (DE-588)4139152-4 gnd |
| topic_facet | MATHEMATICS / Applied Numerical calculations Verification Science Data processing Numerische Mathematik Intervallalgebra |
| url | https://doi.org/10.1515/9781400838974 |
| work_keys_str_mv | AT tuckerwarwick validatednumericsashortintroductiontorigorouscomputations |