Fast automatic differentiation for vector processors and reduction of the spatial complexity in a source translation environment:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
1993
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 117 S. graph. Darst. |
Internformat
MARC
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| 100 | 1 | |a Shiriaev, Dmitri V. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Fast automatic differentiation for vector processors and reduction of the spatial complexity in a source translation environment |c von Dmitri V. Shiriaev |
| 264 | 1 | |c 1993 | |
| 300 | |a 117 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |a Karlsruhe, Univ., Diss., 1993 | ||
| 650 | 0 | 7 | |a Automatische Differentiation |0 (DE-588)4314524-3 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Automatische Differentiation |0 (DE-588)4314524-3 |D s |
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Datensatz im Suchindex
| _version_ | 1807594596251729920 |
|---|---|
| adam_text |
CONTENTS
PREFACE
5
1
BASIC
NOTIONS
10
YY1.1
COMPUTER
ARITHMETIC
.
10
1.2
INTERVAL
ARITHMETIC
.
13
1.3
DIFFERENTIATION
ARITHMETIC
.
15
1.4
TAYLOR
ARITHMETIC
.
18
1.5
LANGUAGES
FOR
SCIENTIFIC
COMPUTING
.
21
2
FAST
AUTOMATIC
DIFFERENTIATION
AND
APPLICATIONS
23
2.1
MOTIVATION
.
23
2.2
THE
GENERAL
SCHEME
.
24
2.2.1
THE
COMPLEXITY
OF
FAST
AUTOMATIC
DIFFERENTIATION
.
27
2.2.2
REVERSE
MODE
FOR
AT
MOST
BINARY
BASIC
FUNCTIONS
.
28
2.3
RELATIONSHIP
TO
THE
SHORTCST-PATH
PROBLEM
IN
A
GRAPH
.
30
2.3.1
DEFINITIONS
.
30
2.3.2
THE
COMPUTATIONAL
GRAPH
.
32
2.3.3
SINGLE-SOURCE
SHORTEST
PATH
IN
A
COMPUTATIONAL
GRAPH
.
33
2.3.4
COMPLEXITY
OF
TRAVERSING
A
COMPUTATIONAL
GRAPH
.
35
2.4
COMPUTATION
OF
THE
JACOBIAN
MATRIX
.
36
2.5
FAST
COMPUTATION
OF
THE
HESSIAN
MATRIX
.
.
.
37
2.6
LOGARITHMIC
SPATIAL
AND
TEMPORAL
COMPLEXITY
.
40
2.7
OPTIMAL
RANGE
COMPUTATION
AND
ESTIMATION
OF
ROUNDOFF,ERRORS
.
42
2.8
A
SURVEY
OF
AUTOMATIC
DIFFERENTIATION
SYSTEMS
.
45
3
FAST
AUTOMATIC
DIFFERENTIATION
FOR
VECTOR
PROCESSOR*
47
3.1
DEFINITION
OF
EXTENDED
OPERATIONS
.
48
3.2
OPTIMAL
DOT
PRODUCT
.
;
.
,
.
50
3.2.1
COMPLEXITY
ESTIMATION
.
52
3.2.2
MATRIX
MULTIPLICATION
.
53
34
LANGUAGE
SUPPORT
FOR
VECTOR
OPERATIONS
.
56
3.3.1
FLEXIBLE
ARRAYS
.
58
3.4
THE
C++
BASED
IMPLEMENTATIONS
.
58
3.5
OPTIMAL
GRADIENT
COMPUTATION
FOR
THE
HELMHOLTZ
FUNCTION
.
70
3.6
COMPARISON
FOR
DIFFERENT
IMPLEMENTATIONS
.
73
3.7
CONCLUSION
.
.
75
4
REDUCTION
OF
SPATIAL
COMPLEXITY
BY
INVERTED
CODE
76
4.1
THE
IDEA
OF
PROGRAM
CONTROL-FLOW
INVERSION
.
77
4.2
INVERSION
OF
STATEMENTS
.
78
4.2.1
INVERSION
OF
LOOPS
.
'.
.
.
.
79
4.2.2
ASSIGNMENTS
.
-.
.
.
'
.
81
4.24
NONINVERTIBLE
ASSIGNMENTS
.
82
4.2.4
INVERTIBLE
ASSIGNMENTS
,
.
84
.
4.3
EXAMPLES
OF
THE
INVERTED
CODE
.
87
4.3.1
DERIVATIVE
OF
/()
YY
*YY
.
.
.
.YY
.
87
4.3.2
DERIVATIVE
OF
A
POLYNOMIAL
.
89
444
OPTIMAL
GRADIENT
COMPUTATION
FOR
A
DETERMINANT
.
91
4.4
NUMERICAL
ASPECTS
OF
THE
RESTORATION
.
93
5
ON
THE
"
TOTALITY
"
OF
STRAIGHT-LINE
PROGRAMS
94
5.1
SOME
KNOWN
RESULTS
ON
STRAIGHT-LINE
PROGRAMS
.
95
5.2
PROGRAMS
WITH
DIVISION
.
*
.
97
A
GRADIENT
COMPUTATION
FOR
THE
HELMHOLTS
ENERGY
FUNCTION
IM
A.L
TEMPLATE
CLASS
FOR
SIMPLE
DYNAMIC
ARRAYS
.
103
A.2
GRADIENT
COMPUTATION
FOR
THE
HDMHOLTI
ENERGY
FUNCTION
USING
RAD
CLASS
.
106
A4
GRADIENT
COMPUTATION
FOR
THE
HELMHOLTS
ENERGY
FUNCTION
USING
VMRAD
CLASS
.
108
BIBLIOGRAPHY
IM |
| any_adam_object | 1 |
| author | Shiriaev, Dmitri V. |
| author_facet | Shiriaev, Dmitri V. |
| author_role | aut |
| author_sort | Shiriaev, Dmitri V. |
| author_variant | d v s dv dvs |
| building | Verbundindex |
| bvnumber | BV009792266 |
| classification_tum | DAT 544d DAT 516d DAT 214d |
| ctrlnum | (OCoLC)52253412 (DE-599)BVBBV009792266 |
| discipline | Informatik |
| format | Thesis Book |
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| illustrated | Illustrated |
| indexdate | 2024-08-17T01:02:19Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006478195 |
| oclc_num | 52253412 |
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| physical | 117 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
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| spelling | Shiriaev, Dmitri V. Verfasser aut Fast automatic differentiation for vector processors and reduction of the spatial complexity in a source translation environment von Dmitri V. Shiriaev 1993 117 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Karlsruhe, Univ., Diss., 1993 Automatische Differentiation (DE-588)4314524-3 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Automatische Differentiation (DE-588)4314524-3 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006478195&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shiriaev, Dmitri V. Fast automatic differentiation for vector processors and reduction of the spatial complexity in a source translation environment Automatische Differentiation (DE-588)4314524-3 gnd |
| subject_GND | (DE-588)4314524-3 (DE-588)4113937-9 |
| title | Fast automatic differentiation for vector processors and reduction of the spatial complexity in a source translation environment |
| title_auth | Fast automatic differentiation for vector processors and reduction of the spatial complexity in a source translation environment |
| title_exact_search | Fast automatic differentiation for vector processors and reduction of the spatial complexity in a source translation environment |
| title_full | Fast automatic differentiation for vector processors and reduction of the spatial complexity in a source translation environment von Dmitri V. Shiriaev |
| title_fullStr | Fast automatic differentiation for vector processors and reduction of the spatial complexity in a source translation environment von Dmitri V. Shiriaev |
| title_full_unstemmed | Fast automatic differentiation for vector processors and reduction of the spatial complexity in a source translation environment von Dmitri V. Shiriaev |
| title_short | Fast automatic differentiation for vector processors and reduction of the spatial complexity in a source translation environment |
| title_sort | fast automatic differentiation for vector processors and reduction of the spatial complexity in a source translation environment |
| topic | Automatische Differentiation (DE-588)4314524-3 gnd |
| topic_facet | Automatische Differentiation Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006478195&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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