The science of programming matrix computations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
[S.l.]
Www.lulu.com
2008
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | "Draft edition, January 2008." |
| Beschreibung: | VIII, 128 S. Ill., graph. Darst. 28 cm |
Internformat
MARC
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| 007 | t | ||
| 008 | 130207s2008 ad|| |||| 00||| eng d | ||
| 020 | |z 2000319094613 |9 200-0-3190946-1-3 | ||
| 035 | |a (OCoLC)828795209 | ||
| 035 | |a (DE-599)BVBBV040734852 | ||
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| 041 | 0 | |a eng | |
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| 084 | |a SK 220 |0 (DE-625)143224: |2 rvk | ||
| 100 | 1 | |a Van De Geijn, Robert A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The science of programming matrix computations |c Robert A. Van de Geijn ; Enrique S. Quintana-Ortí |
| 264 | 1 | |a [S.l.] |b Www.lulu.com |c 2008 | |
| 300 | |a VIII, 128 S. |b Ill., graph. Darst. |c 28 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a "Draft edition, January 2008." | ||
| 650 | 4 | |a Matrices / Data processing | |
| 650 | 4 | |a Algebras, Linear | |
| 650 | 4 | |a High performance computing / Linear programming | |
| 650 | 4 | |a Datenverarbeitung | |
| 700 | 1 | |a Quintana-Ortí, Enrique S. |e Sonstige |4 oth | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025714921&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-025714921 | ||
Datensatz im Suchindex
| _version_ | 1804150052880384000 |
|---|---|
| adam_text | Contents
List of Contributors
iii
Preface
v
1
Motivation
1
1.1
A Motivating Example: the
LU
Factorization
............................. 1
1.2
Notation
.................................................. 1
1.3
Algorithmic Variants
........................................... 2
1.4
Presenting Algorithms in Code
..................................... 4
1.5
High Performance and Blocked Algorithms
.............................. 5
1.6
Numerical Stability
............................................ 6
2
Derivation of Linear Algebra Algorithms
7
2.1
A Farewell to Indices
........................................... 7
2.2
Predicates as Assertions about the State
................................ 9
2.3
Verifying Loops
.............................................. 10
2.4
Goal-Oriented Derivation of Algorithms
................................ 12
2.5
Cost Analysis
............................................... 16
2.6
Summary
................................................. 17
2.7
Other Vector-Vector Operations
..................................... 18
2.8
Further Exercises
............................................. 18
3
Matrix-Vector Operations
19
3.1
Notation
.................................................. 19
3.2
Linear Transformations and Matrices
.................................. 20
3.3
Algorithms for the Matrix-Vector Product
............................... 24
3.4
Rank-1 Update
.............................................. 28
3.5
Solving Triangular Linear Systems of Equations
............................ 31
3.6
Blocked Algorithms
............................................ 38
3.7
Summary
................................................. 43
3.8
Other Matrix-Vector Operations
.................................... 43
3.9
Further Exercises
............................................. 43
4
The FLAME Application Programming Interfaces
45
4.1
Example: GEMV Revisited
........................................ 45
4.2
The FLAME@lab Interface for M-script
............................... 45
4.3
The FLAME/C Interface for the
С
Programming Language
.................... 52
4.4
Summary
................................................. 63
4.5
Further Exercises
............................................. 63
High Performance Algorithms
65
5.1
Architectural Considerations
...................................... 65
5.2
Matrix-Matrix Product: Background
................................. 66
5.3
Algorithms for
gemm
.......................................... 70
5.4
High-Performance Implementation of GEPP, gemp, and gepm
.................... 74
5.5
Modularity and Performance via
GEMM:
Implementing SYMM
.................... 78
5.6
Summary
................................................. 82
5.7
Other Matrix-Matrix Operations
.................................... 82
5.8
Further Exercises
............................................. 82
The
LU
and Cholesky Factorizations
85
6.1
Gaussian Elimination
........................................... 85
6.2
The
LU
Factorization
.......................................... 86
6.3
The Basics of Partial Pivoting
...................................... 92
6.4
Partial Pivoting and High Performance
................................. 95
6.5
The Cholesky Factorization
....................................... 101
6.6
Summary
................................................. 103
6.7
Further Exercises
............................................. 103
The New Frontier
105
7.1
What is the Scope of the Notation and
Methodolog} ?........................ 105
7.2
What Languages can be Targeted?
................................... 105
7.3
What Architectures can be Targeted?
................................. 106
7.4
The Final Generation of Dense and Banded Linear Algebra Library
................ 106
The Use of Letters
107
Summary of FLAME/C Routines
109
B.I Parameters
................................................ 109
B.2 Initializing and Finalizing FLAME/C
................................. 110
B.3 Manipulating Linear Algebra Objects
.................................
Ill
B.4 Printing the Contents of an Object
................................... 112
B.5 A Subset of Supported Operations
................................... 112
|
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| id | DE-604.BV040734852 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:32:48Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025714921 |
| oclc_num | 828795209 |
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| physical | VIII, 128 S. Ill., graph. Darst. 28 cm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Www.lulu.com |
| record_format | marc |
| spelling | Van De Geijn, Robert A. Verfasser aut The science of programming matrix computations Robert A. Van de Geijn ; Enrique S. Quintana-Ortí [S.l.] Www.lulu.com 2008 VIII, 128 S. Ill., graph. Darst. 28 cm txt rdacontent n rdamedia nc rdacarrier "Draft edition, January 2008." Matrices / Data processing Algebras, Linear High performance computing / Linear programming Datenverarbeitung Quintana-Ortí, Enrique S. Sonstige oth Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025714921&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Van De Geijn, Robert A. The science of programming matrix computations Matrices / Data processing Algebras, Linear High performance computing / Linear programming Datenverarbeitung |
| title | The science of programming matrix computations |
| title_auth | The science of programming matrix computations |
| title_exact_search | The science of programming matrix computations |
| title_full | The science of programming matrix computations Robert A. Van de Geijn ; Enrique S. Quintana-Ortí |
| title_fullStr | The science of programming matrix computations Robert A. Van de Geijn ; Enrique S. Quintana-Ortí |
| title_full_unstemmed | The science of programming matrix computations Robert A. Van de Geijn ; Enrique S. Quintana-Ortí |
| title_short | The science of programming matrix computations |
| title_sort | the science of programming matrix computations |
| topic | Matrices / Data processing Algebras, Linear High performance computing / Linear programming Datenverarbeitung |
| topic_facet | Matrices / Data processing Algebras, Linear High performance computing / Linear programming Datenverarbeitung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025714921&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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