Variable dimension fixed point algorithms and triangulations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam
Mathematisch Centrum
1980
|
| Series: | Mathematisch Centrum <Amsterdam>: Mathematical Centre tracts
128 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IV, 172 S. graph. Darst. |
Staff View
MARC
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| 245 | 1 | 0 | |a Variable dimension fixed point algorithms and triangulations |c A. J. Talman. With the collaboration of G. van der Laan |
| 264 | 1 | |a Amsterdam |b Mathematisch Centrum |c 1980 | |
| 300 | |a IV, 172 S. |b graph. Darst. | ||
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| 490 | 1 | |a Mathematisch Centrum <Amsterdam>: Mathematical Centre tracts |v 128 | |
| 650 | 4 | |a Algorithmes | |
| 650 | 4 | |a Point fixe, Théorème du | |
| 650 | 4 | |a Triangulation | |
| 650 | 4 | |a Fixed point theory | |
| 810 | 2 | |a Mathematisch Centrum <Amsterdam> |t Mathematical Centre tracts |v 128 |w (DE-604)BV000893527 |9 128 | |
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Record in the Search Index
| _version_ | 1804118851293544448 |
|---|---|
| adam_text | Ill
CONTENTS
CHAPTER 1. INTRODUCTION AND SUMMARY. 1
CHAPTER 2. PRELIMINARIES. 6
2.1. Introduction. 6
2.2. Triangulations and subdivisions. 6
2.3. Brouwer s theorem and Sperner s lemma. 11
2.4. Kakutani s theorem. 13
2.5. Special triangulations of R . 16
2.6. Triangulations of s . 20
CHAPTER 3. EXTENSIONS AND APPLICATIONS OF FIXED POINT THEOREMS. 26
3.1. Introduction. 26
3.2. Noncooperative N person game. 26
3.3. Extensions to Kakutani s theorem. 28
3.4. constrained optimization. 30
3.5. Nonlinear complementarity problem. 32
CHAPTER 4. ALGORITHMS TO FIND COMPLETELY LABELLED SIMPLICES. 37
4.1. Introduction. 37
4.2. Labelling and accuracy. 38
4.3. Kuhn s and Eaves first algorithms. 44
4.4. Merrill s algorithm. 49
4.5. Van der Laan and Talman s basic algorithm. 52
CHAPTER 5. THE EFFICIENCY OF TRIANGULATIONS. 59
5.1. Introduction. 59
5.2. Fixed point triangulations of Rn. 60
5.3. Crude measures. 63
5.4. Average directional density. 64
5.5. Measures based on minimizing the number of grid points. 69
5.6. Comparison of several triangulations of R . 76
5.7. A good triangulation of the affine hull of S . 80
CHAPTER 6. VARIABLE DIMENSION FIXED POINT ALGORITHM ON THE PRODUCT
SPACE S OF UNIT SIMPLICES. 85
6.1. Introduction. 85
6.2. Triangulation of S. 87
6.3. Integer labelling and approximation. 96
6.4. The variable dimension algorithm on S. 99
6.5. Vector labelling. 105
6.6. Computational experience. 112
CHAPTER 7. CLASS OF VARIABLE DIMENSION FIXED POINT ALGORITHMS ON r . 116
7.1. Introduction. 116
7.2. Triangulation of R for given positive integers
summing up to n. 117
7.3. Integer labelling and approximation. 120
7.4. The variable dimension algorithm on R . 123
7.5. Vector labelling. 128
7.6. The two extreme cases N = 1 and N = n. 133
7.7. Computational experience. 147
CHAPTER 8. GEOMETRIC INTERPRETATIONS OF THE ALGORITHMS. 150
8.1. Introduction. 150
8.2. Interpretation with the set S on the zero level. 151
8.3. Two interpretations with M + N points. 155
8.4. Modification for the algorithm on Rn. 159
REFERENCES. • 165
|
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| id | DE-604.BV004732558 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:16:52Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002911052 |
| oclc_num | 7288695 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-83 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-83 DE-188 |
| physical | IV, 172 S. graph. Darst. |
| publishDate | 1980 |
| publishDateSearch | 1980 |
| publishDateSort | 1980 |
| publisher | Mathematisch Centrum |
| record_format | marc |
| series2 | Mathematisch Centrum <Amsterdam>: Mathematical Centre tracts |
| spelling | Talman, Dolf 1952- Verfasser (DE-588)12235365X aut Variable dimension fixed point algorithms and triangulations A. J. Talman. With the collaboration of G. van der Laan Amsterdam Mathematisch Centrum 1980 IV, 172 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematisch Centrum <Amsterdam>: Mathematical Centre tracts 128 Algorithmes Point fixe, Théorème du Triangulation Fixed point theory Mathematisch Centrum <Amsterdam> Mathematical Centre tracts 128 (DE-604)BV000893527 128 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002911052&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Talman, Dolf 1952- Variable dimension fixed point algorithms and triangulations Algorithmes Point fixe, Théorème du Triangulation Fixed point theory |
| title | Variable dimension fixed point algorithms and triangulations |
| title_auth | Variable dimension fixed point algorithms and triangulations |
| title_exact_search | Variable dimension fixed point algorithms and triangulations |
| title_full | Variable dimension fixed point algorithms and triangulations A. J. Talman. With the collaboration of G. van der Laan |
| title_fullStr | Variable dimension fixed point algorithms and triangulations A. J. Talman. With the collaboration of G. van der Laan |
| title_full_unstemmed | Variable dimension fixed point algorithms and triangulations A. J. Talman. With the collaboration of G. van der Laan |
| title_short | Variable dimension fixed point algorithms and triangulations |
| title_sort | variable dimension fixed point algorithms and triangulations |
| topic | Algorithmes Point fixe, Théorème du Triangulation Fixed point theory |
| topic_facet | Algorithmes Point fixe, Théorème du Triangulation Fixed point theory |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002911052&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000893527 |
| work_keys_str_mv | AT talmandolf variabledimensionfixedpointalgorithmsandtriangulations |