Algorithmic problems in Brunn-Minkowski theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
1995
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 153 S. |
Staff View
MARC
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| 245 | 1 | 0 | |a Algorithmic problems in Brunn-Minkowski theory |c von Alexander Hufnagel |
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Record in the Search Index
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|---|---|
| adam_text |
CONTENTS
INTRODUCTION
V
CHAPTER
I.
PRELIMINARIES
1
1.1.
BASIC
CONVEXITY
1
1.2.
THE
MODEL
OF
COMPUTATION
5
1.3.
PRESENTATION
OF
CONVEX
BODIES
9
CHAPTER
II.
BRUNN-MINKOWSKI
THEORY
19
2.1.
MIXED
VOLUMES
AND
RELATED
CONCEPTS
19
2.2.
INEQUALITIES
BETWEEN
MIXED
VOLUMES
25
2.3.
MINKOWSKI
'
S
RECONSTRUCTION
THEOREM
27
CHAPTER
III.
COMPUTATIONAL
PROBLEMS
IN
BRUNN-MINKOWSKI
THEORY
31
3.1.
POLYTOPE
VOLUME
COMPUTATION
31
II
CONTENTS
3.2.
ESTIMATING
THE
VOLUME
OF
CONVEX
BODIES
36
3.3.
VOLUME
AND
LATTICE
POINTS
39
3.4.
VOLUME
AND
MIXED
VOLUME
COMPUTATION
42
3.5.
SOME
ESTIMATES
FOR
NUMERICAL
DIFFERENTIATION
44
3.6.
MINKOWSKI-PRESENTATION
OF
POLYTOPES
48
CHAPTER
IV.
DETERMINISTIC
ALGORITHMS
FOR
MIXED
VOLUMES
53
4.1.
COMPUTING
THE
VOLUME
OF
ZONOTOPES
53
4.2.
MIXED
VOLUMES
OF
PARALLELOTOPES
59
4.3.
EASINESS
OF
MIXED
VOLUME
COMPUTATION
66
4.4.
APPROXIMATING
MIXED
VOLUMES
75
CHAPTER
V.
RANDOMIZED
ALGORITHMS
FOR
MIXED
VOLUMES
87
5.1.
RELATIVE
ESTIMATES
FOR
MIXED
VOLUMES
88
5.2.
MIXED
VOLUMES
OF
TWO
BODIES
93
5.3.
EXTENSION
TO
MORE
THAN
TWO
BODIES
98
CHAPTER
VI.
TRACTABILITY
OF
MINKOWSKI-RECONSTRUCTION
103
6.1.
A
CONVEX
OPTIMIZATION
PROBLEM
104
6.2.
BOUNDS
FOR
THE
SOLUTIONS
OF
M
INK
C
ONV
M
IN
107
6.3.
MINKOWSKI-OPTIMIZATION
USING
A
VOLUME
ORACLE
110
6.4.
FROM
OPTIMIZATION
TO
HAUSDORFF-APPROXIMATION
112
6.5.
FROM
HAUSDORFF
TO
MINKOWSKI
117
CONTENTS
III
CHAPTER
VII.
HARDNESS
OF
MINKOWSKI-RECONSTRUCTION
121
7.1.
VOLUME
APPROXIMATION
FROM
MEMBERSHIP
122
7.2.
HARDNESS
OF
MINKOWSKI-OPTIMIZATION
123
7.3.
FROM
MINKOWSKI
TO
WEAK
OPTIMIZATION
126
CHAPTER
VIII.
RELATED
PROBLEMS
AND
APPLICATIONS
129
8.1.
SOME
DETERMINANT
PROBLEMS
AND
THEIR
RELATIVES
129
8.2.
VOLUME
OF
ZONOTOPES
AND
MIXTURE
MANAGEMENT
131
8.3.
IMAGE
RECOGNITION
132
8.4.
MIXED
VOLUMES
AND
ALGEBRAIC
GEOMETRY
133
8.5.
FURTHER
APPLICATIONS
OF
MIXED
VOLUMES
142
BIBLIOGRAPHY
145 |
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| discipline | Mathematik |
| format | Thesis Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-08-16T00:35:25Z |
| institution | BVB |
| language | English |
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| physical | XVIII, 153 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| record_format | marc |
| spelling | Hufnagel, Alexander Verfasser aut Algorithmic problems in Brunn-Minkowski theory von Alexander Hufnagel 1995 XVIII, 153 S. txt rdacontent n rdamedia nc rdacarrier Trier, Univ., Diss., 1995 Konvexer Körper (DE-588)4165214-9 gnd rswk-swf Brunn-Minkowski-Satz (DE-588)4333020-4 gnd rswk-swf Berechnungskomplexität (DE-588)4134751-1 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Brunn-Minkowski-Satz (DE-588)4333020-4 s DE-604 Konvexer Körper (DE-588)4165214-9 s Algorithmus (DE-588)4001183-5 s Berechnungskomplexität (DE-588)4134751-1 s DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007086832&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hufnagel, Alexander Algorithmic problems in Brunn-Minkowski theory Konvexer Körper (DE-588)4165214-9 gnd Brunn-Minkowski-Satz (DE-588)4333020-4 gnd Berechnungskomplexität (DE-588)4134751-1 gnd Algorithmus (DE-588)4001183-5 gnd |
| subject_GND | (DE-588)4165214-9 (DE-588)4333020-4 (DE-588)4134751-1 (DE-588)4001183-5 (DE-588)4113937-9 |
| title | Algorithmic problems in Brunn-Minkowski theory |
| title_auth | Algorithmic problems in Brunn-Minkowski theory |
| title_exact_search | Algorithmic problems in Brunn-Minkowski theory |
| title_full | Algorithmic problems in Brunn-Minkowski theory von Alexander Hufnagel |
| title_fullStr | Algorithmic problems in Brunn-Minkowski theory von Alexander Hufnagel |
| title_full_unstemmed | Algorithmic problems in Brunn-Minkowski theory von Alexander Hufnagel |
| title_short | Algorithmic problems in Brunn-Minkowski theory |
| title_sort | algorithmic problems in brunn minkowski theory |
| topic | Konvexer Körper (DE-588)4165214-9 gnd Brunn-Minkowski-Satz (DE-588)4333020-4 gnd Berechnungskomplexität (DE-588)4134751-1 gnd Algorithmus (DE-588)4001183-5 gnd |
| topic_facet | Konvexer Körper Brunn-Minkowski-Satz Berechnungskomplexität Algorithmus Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007086832&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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