Computer arithmetic and validity: theory, implementation, and applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
De Gruyter
2008
|
| Schriftenreihe: | De Gruyter studies in mathematics
33 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XVII, 409 S. Illustrationen |
| ISBN: | 9783110203189 |
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Datensatz im Suchindex
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| adam_text |
GESCANNT DURCH CONTENTS PREFACE XI INTRODUCTION 1 I THEORY OF COMPUTER
ARITHMETIC 11 1 FIRST CONCEPTS 12 1.1 ORDEREDSETS 12 1.2 COMPLETE
LATTICES AND COMPLETE SUBNETS 17 1.3 SCREENS AND ROUNDINGS 23 1.4
ARITHMETIC OPERATIONS AND ROUNDINGS 34 2 RINGOIDS AND VECTOIDS 42 2.1
RINGOIDS 42 2.2 VECTOIDS 53 3 DEFINITION OF COMPUTER ARITHMETIC 60 3.1
INTRODUCTION 60 3.2 PRELIMINARIES 62 3.3 THE TRADITIONAL DEFINITION OF
COMPUTER ARITHMETIC 67 3.4 DEFINITION OF COMPUTER ARITHMETIC BY
SEMIMORPHISMS 69 3.5 A REMARK ABOUT ROUNDINGS 75 3.6 UNIQUENESS OF THE
MINUS OPERATOR 77 3.7 ROUNDING NEAR ZERO 79 4 INTERVAL ARITHMETIC 84 4.1
INTERVAL SETS AND ARITHMETIC 84 4.2 INTERVAL ARITHMETIC OVER A LINEARLY
ORDERED SET 94 4.3 INTERVAL MATRICES 98 4.4 INTERVAL VECTORS 103 4.5
INTERVAL ARITHMETIC ON A SCREEN 106 4.6 INTERVAL MATRICES AND INTERVAL
VECTORS ON A SCREEN 114 4.7 COMPLEX INTERVAL ARITHMETIC 122 4.8 COMPLEX
INTERVAL MATRICES AND INTERVAL VECTORS 129 4.9 EXTENDED INTERVAL
ARITHMETIC 134 4.10 EXCEPTION-FREE ARITHMETIC FOR EXTENDED INTERVALS 140
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/988967162 DIGITALISIERT
DURCH * * * * * * X CONTENTS 9.6.1 COMPLETE EXPRESSIONS 336 9.6.2
ACCURATE EVALUATION OF POLYNOMIALS 337 9.6.3 ARITHMETIC EXPRESSIONS 341
9.7 MULTIPLE PRECISION ARITHMETICS 343 9.7.1 MULTIPLE PRECISION
FLOATING-POINT ARITHMETIC 344 9.7.2 MULTIPLE PRECISION INTERVAL
ARITHMETIC 347 9.7.3 APPLICATIONS 352 9.7.4 ADDING AN EXPONENT PART AS A
SCALING FACTOR TO COMPLETE ARITHMETIC 354 A FREQUENTLY USED SYMBOLS 356
B ON HOMOMORPHISM 358 BIBLIOGRAPHY 359 LISTOFFIGURES 395 LISTOFTABLES
399 INDEX 401 |
| adam_txt |
GESCANNT DURCH CONTENTS PREFACE XI INTRODUCTION 1 I THEORY OF COMPUTER
ARITHMETIC 11 1 FIRST CONCEPTS 12 1.1 ORDEREDSETS 12 1.2 COMPLETE
LATTICES AND COMPLETE SUBNETS 17 1.3 SCREENS AND ROUNDINGS 23 1.4
ARITHMETIC OPERATIONS AND ROUNDINGS 34 2 RINGOIDS AND VECTOIDS 42 2.1
RINGOIDS 42 2.2 VECTOIDS 53 3 DEFINITION OF COMPUTER ARITHMETIC 60 3.1
INTRODUCTION 60 3.2 PRELIMINARIES 62 3.3 THE TRADITIONAL DEFINITION OF
COMPUTER ARITHMETIC 67 3.4 DEFINITION OF COMPUTER ARITHMETIC BY
SEMIMORPHISMS 69 3.5 A REMARK ABOUT ROUNDINGS 75 3.6 UNIQUENESS OF THE
MINUS OPERATOR 77 3.7 ROUNDING NEAR ZERO 79 4 INTERVAL ARITHMETIC 84 4.1
INTERVAL SETS AND ARITHMETIC 84 4.2 INTERVAL ARITHMETIC OVER A LINEARLY
ORDERED SET 94 4.3 INTERVAL MATRICES 98 4.4 INTERVAL VECTORS 103 4.5
INTERVAL ARITHMETIC ON A SCREEN 106 4.6 INTERVAL MATRICES AND INTERVAL
VECTORS ON A SCREEN 114 4.7 COMPLEX INTERVAL ARITHMETIC 122 4.8 COMPLEX
INTERVAL MATRICES AND INTERVAL VECTORS 129 4.9 EXTENDED INTERVAL
ARITHMETIC 134 4.10 EXCEPTION-FREE ARITHMETIC FOR EXTENDED INTERVALS 140
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/988967162 DIGITALISIERT
DURCH * * * * * * X CONTENTS 9.6.1 COMPLETE EXPRESSIONS 336 9.6.2
ACCURATE EVALUATION OF POLYNOMIALS 337 9.6.3 ARITHMETIC EXPRESSIONS 341
9.7 MULTIPLE PRECISION ARITHMETICS 343 9.7.1 MULTIPLE PRECISION
FLOATING-POINT ARITHMETIC 344 9.7.2 MULTIPLE PRECISION INTERVAL
ARITHMETIC 347 9.7.3 APPLICATIONS 352 9.7.4 ADDING AN EXPONENT PART AS A
SCALING FACTOR TO COMPLETE ARITHMETIC 354 A FREQUENTLY USED SYMBOLS 356
B ON HOMOMORPHISM 358 BIBLIOGRAPHY 359 LISTOFFIGURES 395 LISTOFTABLES
399 INDEX 401 |
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| dewey-full | 511.42 518.0285 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
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| discipline | Informatik Mathematik |
| discipline_str_mv | Informatik Mathematik |
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| illustrated | Illustrated |
| index_date | 2024-07-02T22:07:31Z |
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| institution | BVB |
| isbn | 9783110203189 |
| language | English |
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| physical | XVII, 409 S. Illustrationen |
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| series | De Gruyter studies in mathematics |
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| spelling | Kulisch, Ulrich 1933- Verfasser (DE-588)105898430 aut Computer arithmetic and validity theory, implementation, and applications Ulrich Kulisch Berlin [u.a.] De Gruyter 2008 XVII, 409 S. Illustrationen txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematics 33 Computer arithmetic Computer arithmetic and logic units Floating-point arithmetic Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Gleitkommarechnung (DE-588)4157582-9 gnd rswk-swf Computerarithmetik (DE-588)4135485-0 gnd rswk-swf Intervallalgebra (DE-588)4139152-4 gnd rswk-swf Richtigkeit von Ergebnissen (DE-588)4127444-1 gnd rswk-swf Computerarithmetik (DE-588)4135485-0 s DE-604 Intervallalgebra (DE-588)4139152-4 s Gleitkommarechnung (DE-588)4157582-9 s Numerische Mathematik (DE-588)4042805-9 s Richtigkeit von Ergebnissen (DE-588)4127444-1 s De Gruyter studies in mathematics 33 (DE-604)BV000005407 33 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3118558&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016750173&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kulisch, Ulrich 1933- Computer arithmetic and validity theory, implementation, and applications De Gruyter studies in mathematics Computer arithmetic Computer arithmetic and logic units Floating-point arithmetic Numerische Mathematik (DE-588)4042805-9 gnd Gleitkommarechnung (DE-588)4157582-9 gnd Computerarithmetik (DE-588)4135485-0 gnd Intervallalgebra (DE-588)4139152-4 gnd Richtigkeit von Ergebnissen (DE-588)4127444-1 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4157582-9 (DE-588)4135485-0 (DE-588)4139152-4 (DE-588)4127444-1 |
| title | Computer arithmetic and validity theory, implementation, and applications |
| title_auth | Computer arithmetic and validity theory, implementation, and applications |
| title_exact_search | Computer arithmetic and validity theory, implementation, and applications |
| title_exact_search_txtP | Computer arithmetic and validity 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_short | Computer arithmetic and validity |
| title_sort | computer arithmetic and validity theory implementation and applications |
| title_sub | theory, implementation, and applications |
| topic | Computer arithmetic Computer arithmetic and logic units Floating-point arithmetic Numerische Mathematik (DE-588)4042805-9 gnd Gleitkommarechnung (DE-588)4157582-9 gnd Computerarithmetik (DE-588)4135485-0 gnd Intervallalgebra (DE-588)4139152-4 gnd Richtigkeit von Ergebnissen (DE-588)4127444-1 gnd |
| topic_facet | Computer arithmetic Computer arithmetic and logic units Floating-point arithmetic Numerische Mathematik Gleitkommarechnung Computerarithmetik Intervallalgebra Richtigkeit von Ergebnissen |
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