Linear algebra over small finite fields on parallel machines
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| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Essen
Fachbereich Math. der Univ. GH
1995
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| Schriftenreihe: | Vorlesungen aus dem Fachbereich Mathematik der Universität GH Essen
23 |
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| Online-Zugang: | Inhaltsverzeichnis |
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| 245 | 1 | 0 | |a Linear algebra over small finite fields on parallel machines |c Peter Fleischmann ... |
| 264 | 1 | |a Essen |b Fachbereich Math. der Univ. GH |c 1995 | |
| 300 | |a VI, 113 S. | ||
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| 490 | 1 | |a Vorlesungen aus dem Fachbereich Mathematik der Universität GH Essen |v 23 | |
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| 700 | 1 | |a Fleischmann, Peter |e Sonstige |4 oth | |
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Datensatz im Suchindex
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| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040020458648 |
| DE-BY-UBR_call_number | 80/SI 713 |
| DE-BY-UBR_katkey | 2225332 |
| DE-BY-UBR_location | 80 |
| DE-BY-UBR_media_number | 069041803326 |
| _version_ | 1822733498647052288 |
| adam_text | Contents
Preface i
Contents iii
List of Symbols v
I Parallel linear algebra 1
1 Parallel Gaussian Elimination over Small Finite Fields 3
1.1 Introduction 3
1.2 Implementation of field elements 4
1.2.1 Implementation of prime fields 4
1.2.2 Implementation of arbitrary fields 8
1.2.3 The concept of preeoinpiitation 9
1 .3 Gaussian elimination 10
1.3.1 Computing the null space 10
1.3.2 Searching foi pivot elements 11
1.3.3 Performing row operations by column operations 13
1.3.4 Matrix partition 15
1.3.5 Eliminating multiple rows in a single turn 16
1.4 Implementation 21
1.4.1 Scaling behaviour 21
1.4.2 Implementation of broadcasts 25
1.4.3 Conclusions 27
2 Constructing invariant subspaces 29
2.1 Introduction 29
2.2 The standard approach 29
2.3 Storing subspaces full versus semi echelon 30
2.4 The parallel algorithm ... 32
3 Norton s Irreducibility Criterion 35
3.1 Application 36
iv Contents
II Diagonalisation algorithms 37
4 Diagonalising and Triangulising Matrices over Rings 39
4.1 Introduction 39
4.2 Greatest common divisor computation 39
4.2.1 Smith s GCD computation 40
4.2.2 Blankcnship s GCD computation 41
4.2.3 Approximate running times for polynomial domains .... 45
4.3 Matrix triangulisntion 49
4.3.1 Running times and coefficient growth 53
4.4 Matrix diagonalisation 53
4.4.1 Running times and coefficient growth 55
4.5 Parallel implementations 55
4.5.1 Data structures 56
4.5.2 Parallel versions of Blankenship s HNF and LHNF algorithm 57
4.5.3 Running times 58
5 Diagonalizing Characteristic Matrices 61
5.1 Introduction 61
5.2 The Reduction Theorem 62
5.3 The Diagonalizing Algorithm 66
5.4 The Invariant Factors 75
5.5 The Rational Canonical Form 85
5.6 Implementation Notes 87
5.7 Running Times 92
III Factorization algorithms 97
6 Implementation of Polynomial Factorization Algorithms 99
6.1 Introduction 99
6.2 Basic concepts 100
6.2.1 Equivalent subspaces 100
6.2.2 Extracting factors and randomization 101
6.2.3 Berlekamp s and Niederreiter s Subspaces 102
6.3 The implementations 104
6.4 Concluding remarks 106
Contact Information 109
Bibliography 111
|
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| id | DE-604.BV010711304 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-23T14:08:53Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007151544 |
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| physical | VI, 113 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Fachbereich Math. der Univ. GH |
| record_format | marc |
| series | Vorlesungen aus dem Fachbereich Mathematik der Universität GH Essen |
| series2 | Vorlesungen aus dem Fachbereich Mathematik der Universität GH Essen |
| spellingShingle | Linear algebra over small finite fields on parallel machines Vorlesungen aus dem Fachbereich Mathematik der Universität GH Essen Galois-Feld (DE-588)4155896-0 gnd Lineare Algebra (DE-588)4035811-2 gnd Paralleler Algorithmus (DE-588)4193615-2 gnd |
| subject_GND | (DE-588)4155896-0 (DE-588)4035811-2 (DE-588)4193615-2 |
| title | Linear algebra over small finite fields on parallel machines |
| title_auth | Linear algebra over small finite fields on parallel machines |
| title_exact_search | Linear algebra over small finite fields on parallel machines |
| title_full | Linear algebra over small finite fields on parallel machines Peter Fleischmann ... |
| title_fullStr | Linear algebra over small finite fields on parallel machines Peter Fleischmann ... |
| title_full_unstemmed | Linear algebra over small finite fields on parallel machines Peter Fleischmann ... |
| title_short | Linear algebra over small finite fields on parallel machines |
| title_sort | linear algebra over small finite fields on parallel machines |
| topic | Galois-Feld (DE-588)4155896-0 gnd Lineare Algebra (DE-588)4035811-2 gnd Paralleler Algorithmus (DE-588)4193615-2 gnd |
| topic_facet | Galois-Feld Lineare Algebra Paralleler Algorithmus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007151544&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT fleischmannpeter linearalgebraoversmallfinitefieldsonparallelmachines |