How to multiply matrices faster:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1984
|
| Schriftenreihe: | Lecture notes in computer science
179 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 212 S. |
| ISBN: | 3540138668 0387138668 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV000234027 | ||
| 003 | DE-604 | ||
| 005 | 20070323 | ||
| 007 | t | ||
| 008 | 870612s1984 |||| 00||| eng d | ||
| 020 | |a 3540138668 |9 3-540-13866-8 | ||
| 020 | |a 0387138668 |9 0-387-13866-8 | ||
| 035 | |a (OCoLC)230633048 | ||
| 035 | |a (DE-599)BVBBV000234027 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-91 |a DE-91G |a DE-384 |a DE-20 |a DE-824 |a DE-29T |a DE-19 |a DE-703 |a DE-739 |a DE-706 |a DE-11 |a DE-188 |a DE-83 | ||
| 084 | |a SS 4800 |0 (DE-625)143528: |2 rvk | ||
| 084 | |a 65F30 |2 msc | ||
| 084 | |a DAT 535f |2 stub | ||
| 084 | |a 68C25 |2 msc | ||
| 100 | 1 | |a Pan, Victor |d 1939- |e Verfasser |0 (DE-588)110340566 |4 aut | |
| 245 | 1 | 0 | |a How to multiply matrices faster |c Victor Pan |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1984 | |
| 300 | |a XI, 212 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in computer science |v 179 | |
| 650 | 0 | 7 | |a Algorithmus |0 (DE-588)4001183-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Matrizenmultiplikation |0 (DE-588)4169129-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Matrizenmultiplikation |0 (DE-588)4169129-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Matrizenmultiplikation |0 (DE-588)4169129-5 |D s |
| 689 | 1 | 1 | |a Algorithmus |0 (DE-588)4001183-5 |D s |
| 689 | 1 | |5 DE-604 | |
| 830 | 0 | |a Lecture notes in computer science |v 179 |w (DE-604)BV000000607 |9 179 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000140241&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-000140241 | ||
Datensatz im Suchindex
| _version_ | 1804114696475770880 |
|---|---|
| adam_text | CONTENTS
SOME NOTATION AND ABBREVIATIONS VII
INTRODUCTION 1
PART 1. THE EXPONENT OF MATRIX MULTIPLICATION 7
Summary 7
1. The Power of Recursive Algorithms for
Matrix Multiplication 7
2. Bilinear Algorithms for MM 9
3. The Search for a Basis Algorithm and the
History of the Asymptotic Acceleration of MM ^ g
4. The Basic Algorithm and the Exponent 2.67 20
5. The Dependence of the Exponent of MM on
the Class of Constants Used 23
6. X algorithms and Their Application to MM.
Accumulation of the Accelerating Power of
A algorithms via Recursion 28
7. Strassen s Conjecture.
Its Extended and Exponential Versions 33
8. Recursive Algorithms for MM and for Disjoint MM
(Definitions, Notation, and Two Basic Facts) 36
9. Some Applications of the Recursive Construction
of Bilinear Algorithms 43
10. Trllinear Versions of Bilinear Algorithms and of
Bilinear X algorithms. Duality.
Recursive Trilinear Algorithms 50
11. Trilinear Aggregating and Some Efficient Basis Designs 56
12. A Further Example of Trilinear Aggregating and
Its Refinement via a Linear Transformation of Variables 58
13 Aggregating the Triplets of Principal Terms 61
11. Recursive Application of Trilinear Aggregating .., 69
15. Can the Exponent Be Further Reduced? 77
16. The Exponents Below 2.5 gg
IV
17. How Much Can We Reduce the Exponent? 89
PART 2. CORRELATION BETWEEN MATRIX MULTIPLICATION AND
OTHER COMPUTATIONAL PROBLEMS.
BIT TIME, BIT SPACE, STABILITY, and CONDITION 95
Summary 95
18. Reduction of Some Combinatorial Computational
Problems to MM 96
19 Asymptotic Arithmetical Complexity of Some Computations
in Linear Algebra 103
20. Two Block Matrix Algorithms for the QR factorization
and QR type Factorization of a Matrix 107
21. Applications of the QR and QR type Factorization
to the Problems MI, SLE, and Det 113
22. Storage Space for Asymptotically Fast Matrix Operations 115
23 The Bit Complexity of Computations in Linear Algebra.
The Case of Matrix Multiplication 117
24. Matrix Norms and Their Application to Estimating
the Bit Complexity of Matrix Multiplication 124
25. Stability and Condition of Algebraic Problems
and of Algorithms for Such Problems 128
26. Estimating the Errors of the QR factorization
of a Matrix 133
27. The Bit Complexity and the Condition of the
Problem of Solving a System of Linear Equations 140
28. The Bit Complexity and the Condition of
the Problem of Matrix Inversion 143
29. The Bit Complexity and the Condition of the
Problem of the Evaluation of the
Determinant of a Matrix 145
30. Summary of the Bounds on the Bit Time of
Computations in Linear Algebra; Acceleration of Solving
a System of Linear Equations Where High
Relative Precision of the Output Is Required 148
V
PART 3 THE SPEED UP OF THE MULTIPLICATION
OF MATRICES OF A FIXED SIZE 153
Summary 153
31. The Currently Best Upper Bounds on the Rank of
the Problem of MM of Moderate Sizes 154
32. Commutative Quadratic Algorithms for MM 162
33. X algorithms for the Multiplication
of Matrices of Small and Moderate Sizes 166
34. The Classes of Straight Line Arithmetical
Algorithms and X algorithms and
Their Reduction to Quadratic Ones 171
35. The Basic Active Substitution Argument and
Lower Bounds on the Ranks of Arithmetical Algorithms
for Matrix Multiplication 175
36. Lower Bounds on the X rank and on
the Commutative X rank of Matrix Multiplication 183
37. Basic Active Substitution Argument and
Lower Bounds on the Number of Additions and Subtractions 187
38. Nonlinear Lower Bounds on the Complexity of
Arithmetical Problems Under Additional
Restrictions on the Computational Schemes 190
39. A Trade off between the Additive Complexity and
the Asynchronicity of Linear and Bilinear Algorithms 193
40. An Attempt of Practical Acceleration of Matrix
Multiplication and of Some Other Arithmetical
Computations 196
APPENDIX . 199
INDEX OF SOME CONCEPTS 201
REFERENCES 205
|
| any_adam_object | 1 |
| author | Pan, Victor 1939- |
| author_GND | (DE-588)110340566 |
| author_facet | Pan, Victor 1939- |
| author_role | aut |
| author_sort | Pan, Victor 1939- |
| author_variant | v p vp |
| building | Verbundindex |
| bvnumber | BV000234027 |
| classification_rvk | SS 4800 |
| classification_tum | DAT 535f |
| ctrlnum | (OCoLC)230633048 (DE-599)BVBBV000234027 |
| discipline | Informatik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01710nam a2200433 cb4500</leader><controlfield tag="001">BV000234027</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20070323 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">870612s1984 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540138668</subfield><subfield code="9">3-540-13866-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387138668</subfield><subfield code="9">0-387-13866-8</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)230633048</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV000234027</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SS 4800</subfield><subfield code="0">(DE-625)143528:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">65F30</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">DAT 535f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">68C25</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Pan, Victor</subfield><subfield code="d">1939-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)110340566</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">How to multiply matrices faster</subfield><subfield code="c">Victor Pan</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">1984</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XI, 212 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Lecture notes in computer science</subfield><subfield code="v">179</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algorithmus</subfield><subfield code="0">(DE-588)4001183-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Matrizenmultiplikation</subfield><subfield code="0">(DE-588)4169129-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Matrizenmultiplikation</subfield><subfield code="0">(DE-588)4169129-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Matrizenmultiplikation</subfield><subfield code="0">(DE-588)4169129-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Algorithmus</subfield><subfield code="0">(DE-588)4001183-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Lecture notes in computer science</subfield><subfield code="v">179</subfield><subfield code="w">(DE-604)BV000000607</subfield><subfield code="9">179</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000140241&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-000140241</subfield></datafield></record></collection> |
| id | DE-604.BV000234027 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:10:49Z |
| institution | BVB |
| isbn | 3540138668 0387138668 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000140241 |
| oclc_num | 230633048 |
| open_access_boolean | |
| owner | DE-12 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-384 DE-20 DE-824 DE-29T DE-19 DE-BY-UBM DE-703 DE-739 DE-706 DE-11 DE-188 DE-83 |
| owner_facet | DE-12 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-384 DE-20 DE-824 DE-29T DE-19 DE-BY-UBM DE-703 DE-739 DE-706 DE-11 DE-188 DE-83 |
| physical | XI, 212 S. |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in computer science |
| series2 | Lecture notes in computer science |
| spelling | Pan, Victor 1939- Verfasser (DE-588)110340566 aut How to multiply matrices faster Victor Pan Berlin [u.a.] Springer 1984 XI, 212 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in computer science 179 Algorithmus (DE-588)4001183-5 gnd rswk-swf Matrizenmultiplikation (DE-588)4169129-5 gnd rswk-swf Matrizenmultiplikation (DE-588)4169129-5 s DE-604 Algorithmus (DE-588)4001183-5 s Lecture notes in computer science 179 (DE-604)BV000000607 179 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000140241&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pan, Victor 1939- How to multiply matrices faster Lecture notes in computer science Algorithmus (DE-588)4001183-5 gnd Matrizenmultiplikation (DE-588)4169129-5 gnd |
| subject_GND | (DE-588)4001183-5 (DE-588)4169129-5 |
| title | How to multiply matrices faster |
| title_auth | How to multiply matrices faster |
| title_exact_search | How to multiply matrices faster |
| title_full | How to multiply matrices faster Victor Pan |
| title_fullStr | How to multiply matrices faster Victor Pan |
| title_full_unstemmed | How to multiply matrices faster Victor Pan |
| title_short | How to multiply matrices faster |
| title_sort | how to multiply matrices faster |
| topic | Algorithmus (DE-588)4001183-5 gnd Matrizenmultiplikation (DE-588)4169129-5 gnd |
| topic_facet | Algorithmus Matrizenmultiplikation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000140241&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000607 |
| work_keys_str_mv | AT panvictor howtomultiplymatricesfaster |