An introduction to inverse algebraic eigenvalue problems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Braunschweig [u.a.]
Vieweg [u.a.]
1998
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | V, 301 S. |
| ISBN: | 3528066849 7301036027 |
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MARC
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Record in the Search Index
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| adam_text | Contents
Preface i
1 Preliminaries 1
1.1 Notation and Definitions 1
1.2 Vector and Matrix Norms . , 4
1.3 Eigenvalues and Eigenvectors 6
1.4 The Singular Value Decomposition 10
1.5 Symmetric Matrices 11
1.6 Vandermonde Matrices 13
1.7 The Kronecker Product 16
1.8 The Implicit Function Theorem 18
1.9 The Derivative of a Simple Eigenvalue 22
Notes and References 32
2 Jacobi Matrix Inverse Eigenvalue Problems 35
2.1 Introduction 35
2.2 Preparation Theorems 37
2.3 Existence and Uniqueness 41
2.4 Sensitivity 45
2.5 Numerical Methods 51
2.5.1 Lanczos Method 51
2.5.2 Orthogonal Reduction Methods 55
2.6 Rank One Update Problem 68
2.7 Persymmetric Problem 70
2.8 Periodic Problem 73
2.9 Double Dimension Problem 80
2.10 Miscellaneous Problems 87
2.10.1 Banded Matrix Inverse Eigenvalue Problem 87
2.10.2 Rank One Modification Problem 90
2.10.3 Construction of a Jacobi Matrix from Its Eigenpairs 91
Notes and References 92
3 Pole Assignment Problems 95
iv CONTENTS
3.1 Introduction 95
3.2 Controllability 97
3.3 Pole Assignment Theorem 102
3.4 Sensitivity Issues 106
3.4.1 The Single input Case 107
3.4.2 The Multi input Case Ill
3.5 Schur Method 117
3.5.1 Preliminary Algorithms 118
3.5.2 Schur Algorithm 123
3.6 Invariant Subspace Method 128
3.6.1 Reduction to Orthogonal Canonical Form 128
3.6.2 The Basic Idea and Techniques 131
3.6.3 Invariant Subspace Algorithm 139
3.7 QR like Method 141
3.7.1 Reduction to Staircase Canonical Form 142
3.7.2 The Basic Idea 144
3.7.3 The Techniques for Assigning Real Poles 146
3.7.4 The Techniques for Assigning Complex Poles 148
3.7.5 QR like Algorithm 161
3.8 Numerical Examples 166
3.9 Robust Pole Assignment Problems 173
3.9.1 Measures of Robustness 173
3.9.2 Formulation I and Numerical Method I 177
3.9.3 Formulation II and Numerical Method II 185
Notes and References 194
4 Additive and Multiplicative Inverse Eigenvalue Problems 197
4.1 Introduction 197
4.2 The Solvability of Two demensional Problems 201
4.3 Necessary Conditions for the Solvability 204
4.4 Sufficient Conditions for the Solvability 210
4.4.1 The Nonsymmetric Case 212
4.4.2 The Symmetric Case 219
4.5 Sensitivity Analysis 235
4.6 Newton like Methods 243
4.6.1 Methods for Solving Problem SG 244
4.6.2 Methods for Solving Problem G 253
4.7 Homotopy Method 256
4.7.1 Homotopy Theory 256
4.7.2 Homotopy Algorithm 259
Notes and References 261
5 Nonnegative Matrix Inverse Eigenvalue Problems 263
5.1 Introduction 263
CONTENTS y
5.2 Perron Frobenius Theorem 264
5.3 The Smallest Realizable Spectral Radius 265
5.4 Symmetric Problem 272
Notes and References 279
Bibliography 281
Index 299
|
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| id | DE-604.BV011570279 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:12:00Z |
| institution | BVB |
| isbn | 3528066849 7301036027 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007790258 |
| oclc_num | 634509994 |
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| physical | V, 301 S. |
| publishDate | 1998 |
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| publisher | Vieweg [u.a.] |
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| spelling | Xu, Shu-fang Verfasser aut An introduction to inverse algebraic eigenvalue problems Shu-fang Xu Braunschweig [u.a.] Vieweg [u.a.] 1998 V, 301 S. txt rdacontent n rdamedia nc rdacarrier Algebra (DE-588)4001156-2 gnd rswk-swf Inverses Eigenwertproblem (DE-588)4162232-7 gnd rswk-swf Inverses Eigenwertproblem (DE-588)4162232-7 s Algebra (DE-588)4001156-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007790258&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Xu, Shu-fang An introduction to inverse algebraic eigenvalue problems Algebra (DE-588)4001156-2 gnd Inverses Eigenwertproblem (DE-588)4162232-7 gnd |
| subject_GND | (DE-588)4001156-2 (DE-588)4162232-7 |
| title | An introduction to inverse algebraic eigenvalue problems |
| title_auth | An introduction to inverse algebraic eigenvalue problems |
| title_exact_search | An introduction to inverse algebraic eigenvalue problems |
| title_full | An introduction to inverse algebraic eigenvalue problems Shu-fang Xu |
| title_fullStr | An introduction to inverse algebraic eigenvalue problems Shu-fang Xu |
| title_full_unstemmed | An introduction to inverse algebraic eigenvalue problems Shu-fang Xu |
| title_short | An introduction to inverse algebraic eigenvalue problems |
| title_sort | an introduction to inverse algebraic eigenvalue problems |
| topic | Algebra (DE-588)4001156-2 gnd Inverses Eigenwertproblem (DE-588)4162232-7 gnd |
| topic_facet | Algebra Inverses Eigenwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007790258&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT xushufang anintroductiontoinversealgebraiceigenvalueproblems |