Some numerical methods for large unsymmetric Eigenproblems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
1994
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 154 S. Ill., graph. Darst. |
Internformat
MARC
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| 100 | 1 | |a Jia, Zhongxiao |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Some numerical methods for large unsymmetric Eigenproblems |c vorgelegt von Zhongxiao Jia |
| 264 | 1 | |c 1994 | |
| 300 | |a 154 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |a Bielefeld, Univ., Diss., 1994 | ||
| 650 | 0 | 7 | |a Matrizen-Eigenwertaufgabe |0 (DE-588)4120715-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lanczos-Verfahren |0 (DE-588)4705970-9 |2 gnd |9 rswk-swf |
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| 689 | 0 | 0 | |a Matrizen-Eigenwertaufgabe |0 (DE-588)4120715-4 |D s |
| 689 | 0 | 1 | |a Lanczos-Verfahren |0 (DE-588)4705970-9 |D s |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-006467018 | |
Datensatz im Suchindex
| _version_ | 1807321059731439616 |
|---|---|
| adam_text |
CONTENTS
1
INTRODUCTION
7
1.1
SOME
SOURCES
OF
PROBLEMS
.
7
1.2
SEVERAL
BASIC
PROJECTION
METHODS
.
8
1.3
THE
FORMULATION
OF
THESIS
.
13
2
THE
CONVERGENCE
OF
GENERALIZED
LANCZOS
METHODS
FOR
LARGE
UNSYM
METRIC
EIGENPROBLEMS
17
2.1
PRELIMINARIES
AND
THE
ARNOLDI
ALGORITHMS
.
18
2.1.1
NOTATION
AND
PRELIMINARIES
.
18
2.1.2
THE
ARNOLDI
ALGORITHMS
.
19
2.2
CONVERGENCE
ANALYSIS
.
21
2.2.1
INEQUALITIES
ON
||(F
-
7R
M
)V?||
.
22
2.2.2
A-PRIORI
THEORETICAL
ERROR
BOUNDS
FOR
EIGENELEMENTS
.
43
2.2.3
THE
PROBLEM
OF
A
BEING
DEROGATORY
.
48
2.3
CONCLUSION
.
49
3
ARNOLDI
TYPE
ALGORITHMS
FOR
LARGE
UNSYMMETRIC
MULTIPLE
EIGENROB
LEMS
50
3.1
NOTATION
AND
BASIC
ALGORITHMS
.
52
3.1.1
NOTATION
.
52
3.1.2
BASIC
ALGORITHMS
.
52
3.2
THEORETICAL
BACKGROUND
.
54
3.3
ARNOLDI
TYPE
ALGORITHMS
.
59
3.4
IMPLEMENTATIONS
.
61
3.5
NUMERICAL
EXPERIMENTS
.
63
3.6
CONCLUSION
AND
REMARKS
.
72
4
GENERALIZED
BLOCK
LANCZOS
METHODS
FOR
LARGE
UNSYMMETRIC
EIGEN
PROBLEMS
73
4.1
GENERALIZED
BLOCK
LANCZOS
PROCESS
AND
METHODS
.
74
4.1.1
GENERAL
PROJECTION
PROCESS
AND
NOTATION-THEORETICAL
ASPECTS
.
74
4.1.2
GENERALIZED
BLOCK
LANCZOS
METHODS
.
75
4.2
CONVERGENCE
ANALYSIS
.
76
4.2.1
INEQUALITIES
ON
||(7
-
RR
M
) P||
.
77
4.2.2
A-PRIORI
THEORETICAL
ERROR
BOUNDS
FOR
EIGENELEMENTS
.
84
4.3
THE
BLOCK
ARNOLDI
ALGORITHMS
.
86
4.3.1
THE
DERIVATION
OF
ALGORITHMS
.
86
4.3.2
ALGORITHMS
.
90
4.4
DETAILS
OF
IMPLEMENTATION
.
92
4.4.1
ORTHONORMALIZATION
.
93
4.4.2
NUMERICAL
DEFICIENCY
.
93
4.4.3
CHOICES
OF
INITIAL
V5
.
93
4.4.4
CHOICES
OF
P
AND
M
.
95
4.4.5
MULTIPLE
EIGENVALUES
.
95
4.5
NUMERICAL
EXPERIMENTS
.
96
4.6
CONCLUSION
AND
FUTURE
WORK
.
104
5
BIOMS:
BLOCK
INCOMPLETE
ORTHOGONALIZATION
METHODS
FOR
LARGE
UN
SYMMETRIC
EIGENPROBLEMS
106
5.1
BLOCK
INCOMPLETE
ORTHOGONALIZATION
METHODS
.
107
5.2
PROPERTIES,
RELATIONSHIPS
AND
CONVERGENCE
.
109
5.2.1
BASIC
PROPERTIES
AND
RELATIONSHIPS
.
109
5.2.2
CONVERGENCE
ANALYSIS
.
117
5.3
TWO
ALGORITHMS
.
122
5.4
IMPLEMENTATIONS
.
121
5.4.1
LOCAL
ORTHOGONALITY,
NUMERICAL
DEFICIENCY
AND
CHOICES
OF
T'I
.
.
124
5.4.2
CHOICES
OF
PARAMETERS
I,P
AND
Q
.
124
5.4.3
STOPPING
CRITEIIOU
.
126
5.5
NUMERICAL
EXPERIMENTS
.
127
5.6
CONCLUSIONS
AND
REMARKS
.
131
6
REFINED
ITERATIVE
ALGORITHMS
BASED
ON
ARNOLDI
'
S
PROCESS
FOR
LARGE
UNSYMMETRIC
EIGENPROBLEMS
133
6.1
NEW
STRATEGY
AND
CONVEIGENCE
.
134
6.2
ALGORITHMS
.
137
6.3
PRACTICAL
CONSIDERATIONS
.
138
6.4
NUMERICAL
EXPERIMENTS
.
139
6.5
CONCLUSION
AND
FUTURE
WORK
.
145
BIBLIOGRAPHY
148 |
| any_adam_object | 1 |
| author | Jia, Zhongxiao |
| author_facet | Jia, Zhongxiao |
| author_role | aut |
| author_sort | Jia, Zhongxiao |
| author_variant | z j zj |
| building | Verbundindex |
| bvnumber | BV009774491 |
| classification_tum | MAT 658d |
| ctrlnum | (OCoLC)257652711 (DE-599)BVBBV009774491 |
| discipline | Mathematik |
| format | Thesis Book |
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| genre_facet | Hochschulschrift |
| id | DE-604.BV009774491 |
| illustrated | Illustrated |
| indexdate | 2024-08-14T00:34:35Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006467018 |
| oclc_num | 257652711 |
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| owner_facet | DE-91 DE-BY-TUM DE-29T DE-355 DE-BY-UBR DE-11 DE-188 |
| physical | 154 S. Ill., graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| record_format | marc |
| spelling | Jia, Zhongxiao Verfasser aut Some numerical methods for large unsymmetric Eigenproblems vorgelegt von Zhongxiao Jia 1994 154 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Bielefeld, Univ., Diss., 1994 Matrizen-Eigenwertaufgabe (DE-588)4120715-4 gnd rswk-swf Lanczos-Verfahren (DE-588)4705970-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Matrizen-Eigenwertaufgabe (DE-588)4120715-4 s Lanczos-Verfahren (DE-588)4705970-9 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006467018&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jia, Zhongxiao Some numerical methods for large unsymmetric Eigenproblems Matrizen-Eigenwertaufgabe (DE-588)4120715-4 gnd Lanczos-Verfahren (DE-588)4705970-9 gnd |
| subject_GND | (DE-588)4120715-4 (DE-588)4705970-9 (DE-588)4113937-9 |
| title | Some numerical methods for large unsymmetric Eigenproblems |
| title_auth | Some numerical methods for large unsymmetric Eigenproblems |
| title_exact_search | Some numerical methods for large unsymmetric Eigenproblems |
| title_full | Some numerical methods for large unsymmetric Eigenproblems vorgelegt von Zhongxiao Jia |
| title_fullStr | Some numerical methods for large unsymmetric Eigenproblems vorgelegt von Zhongxiao Jia |
| title_full_unstemmed | Some numerical methods for large unsymmetric Eigenproblems vorgelegt von Zhongxiao Jia |
| title_short | Some numerical methods for large unsymmetric Eigenproblems |
| title_sort | some numerical methods for large unsymmetric eigenproblems |
| topic | Matrizen-Eigenwertaufgabe (DE-588)4120715-4 gnd Lanczos-Verfahren (DE-588)4705970-9 gnd |
| topic_facet | Matrizen-Eigenwertaufgabe Lanczos-Verfahren Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006467018&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT jiazhongxiao somenumericalmethodsforlargeunsymmetriceigenproblems |