Linear algebra over small finite fields on parallel machines:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Essen
Fachbereich Math. der Univ. GH
1995
|
| Series: | Vorlesungen aus dem Fachbereich Mathematik der Universität GH Essen
23 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 113 S. |
Staff View
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| 245 | 1 | 0 | |a Linear algebra over small finite fields on parallel machines |c Peter Fleischmann ... |
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Record in the Search Index
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| 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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| indexdate | 2024-07-09T17:57:37Z |
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| language | English |
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| physical | VI, 113 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
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| 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 |
| spelling | Linear algebra over small finite fields on parallel machines Peter Fleischmann ... Essen Fachbereich Math. der Univ. GH 1995 VI, 113 S. txt rdacontent n rdamedia nc rdacarrier Vorlesungen aus dem Fachbereich Mathematik der Universität GH Essen 23 Galois-Feld (DE-588)4155896-0 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Paralleler Algorithmus (DE-588)4193615-2 gnd rswk-swf Galois-Feld (DE-588)4155896-0 s Lineare Algebra (DE-588)4035811-2 s Paralleler Algorithmus (DE-588)4193615-2 s DE-604 Fleischmann, Peter Sonstige oth Vorlesungen aus dem Fachbereich Mathematik der Universität GH Essen 23 (DE-604)BV010927521 23 HBZ Datenaustausch application/pdf 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 Inhaltsverzeichnis |
| 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 |
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