Computer Arithmetic and Validity : : Theory, Implementation, and Applications / / Ulrich Kulisch.
This is the revised and extended second edition of the successful basic book on computer arithmetic. It is consistent with the newest recent standard developments in the field. The book shows how the arithmetic and mathematical capability of the digital computer can be enhanced in a quite natural wa...
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2013] ©2012 |
Year of Publication: | 2013 |
Language: | English |
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Kulisch, Ulrich, author. aut http://id.loc.gov/vocabulary/relators/aut Computer Arithmetic and Validity : Theory, Implementation, and Applications / Ulrich Kulisch. Berlin ; Boston : De Gruyter, [2013] ©2012 1 online resource (434 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Studies in Mathematics , 0179-0986 ; 33 Frontmatter -- Foreword to the second edition -- Preface -- Contents -- Introduction -- Part I. Theory of computer arithmetic -- Chapter 1. First concepts -- Chapter 2. Ringoids and vectoids -- Chapter 3. Definition of computer arithmetic -- Chapter 4. Interval arithmetic -- Part II. Implementation of arithmetic on computers -- Chapter 5. Floating-point arithmetic -- Chapter 6. Implementation of floating-point arithmetic on a computer -- Chapter 7. Hardware support for interval arithmetic -- Chapter 8. Scalar products and complete arithmetic -- Part III. Principles of verified computing -- Chapter 9. Sample applications -- Appendix A. Frequently used symbols -- Appendix B. On homomorphism -- Bibliography -- List of figures -- List of tables -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star This is the revised and extended second edition of the successful basic book on computer arithmetic. It is consistent with the newest recent standard developments in the field. The book shows how the arithmetic and mathematical capability of the digital computer can be enhanced in a quite natural way. The work is motivated by the desire and the need to improve the accuracy of numerical computing and to control the quality of the computed results (validity). The accuracy requirements for the elementary floating-point operations are extended to the customary product spaces of computations including interval spaces. The mathematical properties of these models are extracted into an axiomatic approach which leads to a general theory of computer arithmetic. Detailed methods and circuits for the implementation of this advanced computer arithmetic on digital computers are developed in part two of the book. Part three then illustrates by a number of sample applications how this extended computer arithmetic can be used to compute highly accurate and mathematically verified results. The book can be used as a high-level undergraduate textbook but also as reference work for research in computer arithmetic and applied mathematics. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. Feb 2023) Computer arithmetic and logic units. Computer arithmetic. Floating-point arithmetic Electronic books. Floating-point arithmetic. Computer Arithmetic. Interval calculation. Numerical Analysis. MATHEMATICS / Number Theory. bisacsh Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package 9783110494938 ZDB-23-GSM Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1 9783110238570 Title is part of eBook package: De Gruyter DGBA Backlist Mathematics 2000-2014 (EN) 9783110238471 Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014 9783110637205 ZDB-23-GMA Title is part of eBook package: De Gruyter E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2013 9783110317350 ZDB-23-DGG Title is part of eBook package: De Gruyter E-BOOK PACKAGE MATHEMATICS, PHYSICS, ENGINEERING 2013 9783110317282 ZDB-23-DMI Title is part of eBook package: De Gruyter E-BOOK PAKET MATHEMATIK, PHYSIK, INGENIEURWISS. 2013 9783110317275 ZDB-23-DMP print 9783110301731 https://doi.org/10.1515/9783110301793 https://www.degruyter.com/isbn/9783110301793 Cover https://www.degruyter.com/document/cover/isbn/9783110301793/original |
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English |
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author |
Kulisch, Ulrich, Kulisch, Ulrich, |
spellingShingle |
Kulisch, Ulrich, Kulisch, Ulrich, Computer Arithmetic and Validity : Theory, Implementation, and Applications / De Gruyter Studies in Mathematics , Frontmatter -- Foreword to the second edition -- Preface -- Contents -- Introduction -- Part I. Theory of computer arithmetic -- Chapter 1. First concepts -- Chapter 2. Ringoids and vectoids -- Chapter 3. Definition of computer arithmetic -- Chapter 4. Interval arithmetic -- Part II. Implementation of arithmetic on computers -- Chapter 5. Floating-point arithmetic -- Chapter 6. Implementation of floating-point arithmetic on a computer -- Chapter 7. Hardware support for interval arithmetic -- Chapter 8. Scalar products and complete arithmetic -- Part III. Principles of verified computing -- Chapter 9. Sample applications -- Appendix A. Frequently used symbols -- Appendix B. On homomorphism -- Bibliography -- List of figures -- List of tables -- Index |
author_facet |
Kulisch, Ulrich, Kulisch, Ulrich, |
author_variant |
u k uk u k uk |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Kulisch, Ulrich, |
title |
Computer Arithmetic and Validity : Theory, Implementation, and Applications / |
title_sub |
Theory, Implementation, and Applications / |
title_full |
Computer Arithmetic and Validity : Theory, Implementation, and Applications / Ulrich Kulisch. |
title_fullStr |
Computer Arithmetic and Validity : Theory, Implementation, and Applications / Ulrich Kulisch. |
title_full_unstemmed |
Computer Arithmetic and Validity : Theory, Implementation, and Applications / Ulrich Kulisch. |
title_auth |
Computer Arithmetic and Validity : Theory, Implementation, and Applications / |
title_alt |
Frontmatter -- Foreword to the second edition -- Preface -- Contents -- Introduction -- Part I. Theory of computer arithmetic -- Chapter 1. First concepts -- Chapter 2. Ringoids and vectoids -- Chapter 3. Definition of computer arithmetic -- Chapter 4. Interval arithmetic -- Part II. Implementation of arithmetic on computers -- Chapter 5. Floating-point arithmetic -- Chapter 6. Implementation of floating-point arithmetic on a computer -- Chapter 7. Hardware support for interval arithmetic -- Chapter 8. Scalar products and complete arithmetic -- Part III. Principles of verified computing -- Chapter 9. Sample applications -- Appendix A. Frequently used symbols -- Appendix B. On homomorphism -- Bibliography -- List of figures -- List of tables -- Index |
title_new |
Computer Arithmetic and Validity : |
title_sort |
computer arithmetic and validity : theory, implementation, and applications / |
series |
De Gruyter Studies in Mathematics , |
series2 |
De Gruyter Studies in Mathematics , |
publisher |
De Gruyter, |
publishDate |
2013 |
physical |
1 online resource (434 p.) Issued also in print. |
contents |
Frontmatter -- Foreword to the second edition -- Preface -- Contents -- Introduction -- Part I. Theory of computer arithmetic -- Chapter 1. First concepts -- Chapter 2. Ringoids and vectoids -- Chapter 3. Definition of computer arithmetic -- Chapter 4. Interval arithmetic -- Part II. Implementation of arithmetic on computers -- Chapter 5. Floating-point arithmetic -- Chapter 6. Implementation of floating-point arithmetic on a computer -- Chapter 7. Hardware support for interval arithmetic -- Chapter 8. Scalar products and complete arithmetic -- Part III. Principles of verified computing -- Chapter 9. Sample applications -- Appendix A. Frequently used symbols -- Appendix B. On homomorphism -- Bibliography -- List of figures -- List of tables -- Index |
isbn |
9783110301793 9783110494938 9783110238570 9783110238471 9783110637205 9783110317350 9783110317282 9783110317275 9783110301731 |
issn |
0179-0986 ; |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA76 |
callnumber-sort |
QA 276.9 C62 K85 42013EB |
url |
https://doi.org/10.1515/9783110301793 https://www.degruyter.com/isbn/9783110301793 https://www.degruyter.com/document/cover/isbn/9783110301793/original |
illustrated |
Not Illustrated |
dewey-hundreds |
000 - Computer science, information & general works |
dewey-tens |
000 - Computer science, knowledge & systems |
dewey-ones |
004 - Data processing & computer science |
dewey-full |
004.0151 |
dewey-sort |
14.0151 |
dewey-raw |
004.0151 |
dewey-search |
004.0151 |
doi_str_mv |
10.1515/9783110301793 |
oclc_num |
953308478 |
work_keys_str_mv |
AT kulischulrich computerarithmeticandvaliditytheoryimplementationandapplications |
status_str |
n |
ids_txt_mv |
(DE-B1597)179444 (OCoLC)953308478 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1 Title is part of eBook package: De Gruyter DGBA Backlist Mathematics 2000-2014 (EN) Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014 Title is part of eBook package: De Gruyter E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2013 Title is part of eBook package: De Gruyter E-BOOK PACKAGE MATHEMATICS, PHYSICS, ENGINEERING 2013 Title is part of eBook package: De Gruyter E-BOOK PAKET MATHEMATIK, PHYSIK, INGENIEURWISS. 2013 |
is_hierarchy_title |
Computer Arithmetic and Validity : Theory, Implementation, and Applications / |
container_title |
Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package |
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1770177529312706560 |
fullrecord |
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