Numerical Toolbox for Verified Computing I: Basic Numerical Problems Theory, Algorithms, and Pascal-XSC Programs
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1993
|
| Series: | Springer Series in Computational Mathematics
21 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | As suggested by the title of this book Numerical Toolbox for Verified Computing, we present an extensive set of sophisticated tools to solve basic numerical problems with a verification of the results. We use the features of the scientific computer language PASCAL-XSC to offer modules that can be combined by the reader to his/her individual needs. Our overriding concern is reliability - the automatic verification of the result a computer returns for a given problem. All algorithms we present are influenced by this central concern. We must point out that there is no relationship between our methods of numerical result verification and the methods of program verification to prove the correctness of an imple~entation for a given algorithm. This book is the first to offer a general discussion on • arithmetic and computational reliability, • analytical mathematics and verification techniques, • algorithms, and • (most importantly) actual implementations in the form of working computer routines. Our task has been to find the right balance among these ingredients for each topic. For some topics, we have placed a little more emphasis on the algorithms. For other topics, where the mathematical prerequisites are universally held, we have tended towards more in-depth discussion of the nature of the computational algorithms, or towards practical questions of implementation. For all topics, we present exam ples, exercises, and numerical results demonstrating the application of the routines presented |
| Physical Description: | 1 Online-Ressource (XV, 339p. 28 illus) |
| ISBN: | 9783642784231 9783642784255 |
| ISSN: | 0179-3632 |
| DOI: | 10.1007/978-3-642-78423-1 |
Staff View
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| id | DE-604.BV042423007 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642784231 9783642784255 |
| issn | 0179-3632 |
| language | English |
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| spelling | Kulisch, Ulrich Verfasser aut Numerical Toolbox for Verified Computing I Basic Numerical Problems Theory, Algorithms, and Pascal-XSC Programs by Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks Berlin, Heidelberg Springer Berlin Heidelberg 1993 1 Online-Ressource (XV, 339p. 28 illus) txt rdacontent c rdamedia cr rdacarrier Springer Series in Computational Mathematics 21 0179-3632 As suggested by the title of this book Numerical Toolbox for Verified Computing, we present an extensive set of sophisticated tools to solve basic numerical problems with a verification of the results. We use the features of the scientific computer language PASCAL-XSC to offer modules that can be combined by the reader to his/her individual needs. Our overriding concern is reliability - the automatic verification of the result a computer returns for a given problem. All algorithms we present are influenced by this central concern. We must point out that there is no relationship between our methods of numerical result verification and the methods of program verification to prove the correctness of an imple~entation for a given algorithm. This book is the first to offer a general discussion on • arithmetic and computational reliability, • analytical mathematics and verification techniques, • algorithms, and • (most importantly) actual implementations in the form of working computer routines. Our task has been to find the right balance among these ingredients for each topic. For some topics, we have placed a little more emphasis on the algorithms. For other topics, where the mathematical prerequisites are universally held, we have tended towards more in-depth discussion of the nature of the computational algorithms, or towards practical questions of implementation. For all topics, we present exam ples, exercises, and numerical results demonstrating the application of the routines presented Mathematics Computer science Numerical analysis Numerical Analysis Programming Techniques Informatik Mathematik Hammer, Rolf Sonstige oth Ratz, Dietmar Sonstige oth Hocks, Matthias Sonstige oth https://doi.org/10.1007/978-3-642-78423-1 Verlag Volltext |
| spellingShingle | Kulisch, Ulrich Numerical Toolbox for Verified Computing I Basic Numerical Problems Theory, Algorithms, and Pascal-XSC Programs Mathematics Computer science Numerical analysis Numerical Analysis Programming Techniques Informatik Mathematik |
| title | Numerical Toolbox for Verified Computing I Basic Numerical Problems Theory, Algorithms, and Pascal-XSC Programs |
| title_auth | Numerical Toolbox for Verified Computing I Basic Numerical Problems Theory, Algorithms, and Pascal-XSC Programs |
| title_exact_search | Numerical Toolbox for Verified Computing I Basic Numerical Problems Theory, Algorithms, and Pascal-XSC Programs |
| title_full | Numerical Toolbox for Verified Computing I Basic Numerical Problems Theory, Algorithms, and Pascal-XSC Programs by Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks |
| title_fullStr | Numerical Toolbox for Verified Computing I Basic Numerical Problems Theory, Algorithms, and Pascal-XSC Programs by Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks |
| title_full_unstemmed | Numerical Toolbox for Verified Computing I Basic Numerical Problems Theory, Algorithms, and Pascal-XSC Programs by Ulrich Kulisch, Rolf Hammer, Dietmar Ratz, Matthias Hocks |
| title_short | Numerical Toolbox for Verified Computing I |
| title_sort | numerical toolbox for verified computing i basic numerical problems theory algorithms and pascal xsc programs |
| title_sub | Basic Numerical Problems Theory, Algorithms, and Pascal-XSC Programs |
| topic | Mathematics Computer science Numerical analysis Numerical Analysis Programming Techniques Informatik Mathematik |
| topic_facet | Mathematics Computer science Numerical analysis Numerical Analysis Programming Techniques Informatik Mathematik |
| url | https://doi.org/10.1007/978-3-642-78423-1 |
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