Perturbation theory for matrix equations:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Amsterdam [u.a.]
Elsevier
2003
|
| Edition: | 1. ed. |
| Series: | Studies in computational mathematics
9 |
| Subjects: | |
| Online Access: | http://www.loc.gov/catdir/enhancements/fy0614/2003053106-d.html Inhaltsverzeichnis |
| Physical Description: | XII, 429 S. graph. Darst. |
| ISBN: | 0444513159 |
Staff View
MARC
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| 245 | 1 | 0 | |a Perturbation theory for matrix equations |c Mihail Konstantinov ... |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Amsterdam [u.a.] |b Elsevier |c 2003 | |
| 300 | |a XII, 429 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Studies in computational mathematics |v 9 | |
| 650 | 4 | |a Matrices | |
| 650 | 4 | |a Perturbation (Mathematics) | |
| 650 | 0 | 7 | |a Matrizengleichung |0 (DE-588)4169125-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Störungstheorie |0 (DE-588)4128420-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Matrizengleichung |0 (DE-588)4169125-8 |D s |
| 689 | 0 | 1 | |a Störungstheorie |0 (DE-588)4128420-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Konstantinov, Mihail |e Sonstige |4 oth | |
| 830 | 0 | |a Studies in computational mathematics |v 9 |w (DE-604)BV001895633 |9 9 | |
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Record in the Search Index
| _version_ | 1804140627057704960 |
|---|---|
| adam_text | Contents
1 Introduction 1
2 Perturbation problems 9
2.1 Introductory remarks 9
2.2 Problem statement 10
2.3 Numerical considerations 18
2.4 Component-wise and backward analysis 20
2.5 Error estimates 24
2.5.1 Forward error 24
2.5.2 Backward error 26
2.6 Scaling 27
2.7 Notes and references 28
3 Problems with explicit Solutions 29
3.1 Introductory remarks 29
3.2 Perturbation function 29
3.3 Regularity and linear bounds 35
3.4 Nonlocal bounds 47
3.5 Case study 48
3.6 Notes and references 50
4 Problems with implicit Solutions 51
4.1 Introductory remarks 51
4.2 Posedness and regularity 51
4.3 Linear bounds 62
4.4 Equivalent Operator equation 64
4.5 Linear equations 67
4.6 Case study 71
4.7 Notes and references 75
vii
viii CONTENTS
5 Lyapunov majorants 77
5.1 Introductory remarks 77
5.2 General theory 77
5.2.1 Polynomial Lyapunov majorants 90
5.2.2 Asymptotic Solutions of polynomial majorant equations . . 96
5.3 Case study 99
5.4 Notes and references 100
6 Singular problems 103
6.1 Introductory remarks 103
6.2 Distance to singularity 104
6.3 Classification 105
6.4 Regularization 108
6.5 Notes and references 111
7 Perturbation bounds 113
7.1 Introductory remarks 113
7.2 Definitions and properties 113
7.3 Conservativeness of worst case bounds 118
7.4 Notes and references 120
8 General Sylvester equations 121
8.1 Introductory remarks 121
8.2 Motivating examples 123
8.3 General linear equations 127
8.4 Perturbation problem 129
8.4.1 Norm-wise perturbations 129
8.4.2 Component-wise perturbations 133
8.4.3 Other perturbations 134
8.5 Local perturbation analysis 136
8.5.1 Norm-wise bounds 136
8.5.2 Component-wise bounds 145
8.6 Nonlocal perturbation analysis 145
8.6.1 Application of the Banach principle 146
8.6.2 Equivalent perturbation Operator 149
8.6.3 Norm-wise bounds 149
8.6.4 Component-wise bounds 152
8.7 Notes and references 153
9 Specific Sylvester equations 155
9.1 Standard linear equation 155
9.2 General equations 168
9.3 Continuous-time equations 168
CONTENTS ix
9.4 Discrete-time equations 171
9.5 Notes and references 172
10 General Lyapunov equations 175
10.1 Introductory remarks 175
10.2 Application to descriptor Systems 175
10.3 Additive matrix Operators 179
10.4 Perturbation problem 187
10.5 Local perturbation analysis 189
10.5.1 Condition numbers 189
10.5.2 First order homogeneous bounds 193
10.5.3 Component-wise bounds 195
10.6 Nonlocal perturbation analysis 195
10.6.1 Real equations 196
10.6.2 Cornplex equations 198
10.6.3 Component-wise bounds 198
10.6.4 Other bounds 200
10.7 Notes and references • 200
11 Lyapunov equations in control tbeory 201
11.1 Introductory remarks 201
11.2 General equation • 201
11.3 Continuous-time equations 203
11.4 Continuous-time equations in descriptor form 210
11.5 Discrete-time equations 216
11 . 6 Discrete-time equations in descriptor form 217
11.7 Notes and references • 221
12 General quadratic equations 223
12.1 Introductory remarks • 223
12.2 Problem Statement • 223
12.3 Motivating example • 227
12.4 Local perturbation analysis . . • 229
12.4.1 Condition numbers 229
12.4.2 First order homogeneous bounds 232
12.4.3 Component-wise bounds • 233
12.5 Nonlocal perturbation analysis ¦ 233
12.6 Notes and references ¦ 238
13 Continuous-time Riccati equations 239
13.1 Introductory remarks ¦ 239
13.2 Motivating example • 239
13 .3 Standard equation 241
x CONTENTS
13.3.1 Statement of the problem 241
13.3.2 Perturbed equation 242
13.3.3 Condition numbers and local bounds 246
13.3.4 Nonlocal bounds 249
13.4 Descriptor equation 255
13.4.1 Statement of the problem 255
13.4.2 Perturbed equation 256
13.4.3 Condition numbers and local bounds 259
13.4.4 Nonlocal bounds 261
13.5 Notes and references 265
14 Coupled Riccati equations 267
14.1 Problem statement 267
14.2 Local perturbation analysis 272
14.2.1 Condition numbers 272
14.2.2 First order homogeneous estimates 276
14.3 Nonlocal perturbation analysis 278
14.3.1 Implicit bounds 278
14.3.2 Explicit bounds 283
14.4 Notes and references 285
15 General fractional-affine equations 287
15.1 Introductory remarks 287
15.2 Problem statement 287
15.3 Local perturbation analysis 291
15.3.1 Condition numbers 292
15.3.2 First order homogeneous bounds 294
15.3.3 Component-wise bounds 295
15.4 Non-local perturbation analysis 295
15.5 Notes and references 302
16 Symmetrie fractional-afHne equations 303
16.1 Introductory remarks 303
16.2 Discrete-time Riccati equations 303
16.2.1 Statement of the problem 303
16.2.2 Motivating example 304
16.2.3 Statement of the problem 305
16.2.4 Perturbed equation 307
16.2.5 Condition numbers and local bounds 310
16.2.6 Nonlocal bounds 312
16.2.7 Complex equation 313
16.2.8 An alternative approach 313
16.2.9 Numerical example 315
CONTENTS xi
16.3 Symmetrie fractional-linear equation 316
16.3.1 Statement of the problem 316
16.3.2 Existence and uniqueness of the solution 317
16.3.3 Local perturbation analysis 320
16.3.4 Nonlocal perturbation analysis 323
16.4 Notes and references 326
A Elements of algebra and analysis 327
A.l Introductory remarks 327
A.2 Sets and funetions 327
A.3 Algebraic Systems 329
A.4 Linear algebra 331
A.5 Normed Spaces 335
A.6 Matrix funetions 337
A.7 Transformation groups 342
A.8 Notes and references 343
B Unitary and orthogonal decompositions 345
B.l Introductory remarks 345
B.2 Elementary unitary matrices 346
B.3 QR decomposition 348
B.4 Schur decomposition 350
B.5 Polar decomposition 352
B.6 Singular value decomposition 354
B.7 Notes and references 355
C Kronecker produet of matrices 357
C.l Introductory remarks 357
C.2 Definitions and properties 357
C.3 Notes and references 361
D Fixed point principles 363
D.l Introductory remarks 363
D.2 Banach principle 363
D.3 Generalized Banach principle 365
D.4 Schauder principle 368
D.5 Notes and references 369
E Sylvester Operators 371
E.l Introductory remarks 371
E.2 Basic coneepts 371
E.3 Representations 373
E.4 Notes and references 377
xii CONTENTS
F Lyapunov Operators 379
F.l Introductory remarks 379
F.2 Real Operators 380
F.3 Complex Operators 389
F.4 Sensitivity and error analysis 394
F.5 Notes and references 395
G Lyapunov-like Operators 397
G.l Introductory remarks 397
G.2 Skew-Lyapunov Operators 397
G.3 Associated Lyapunov Operators 398
G.4 Associated skew-Lyapunov Operators 399
G.5 Notes and references 400
H Notation 401
H.l Sets and spaces 401
H.2 Matrices 402
H.3 Matrix Operators 403
H.4 Norms 404
H.5 Perturbation analysis 405
H.6 Other notation 406
Index 425
|
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| isbn | 0444513159 |
| language | English |
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| owner_facet | DE-83 DE-706 |
| physical | XII, 429 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Elsevier |
| record_format | marc |
| series | Studies in computational mathematics |
| series2 | Studies in computational mathematics |
| spelling | Perturbation theory for matrix equations Mihail Konstantinov ... 1. ed. Amsterdam [u.a.] Elsevier 2003 XII, 429 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Studies in computational mathematics 9 Matrices Perturbation (Mathematics) Matrizengleichung (DE-588)4169125-8 gnd rswk-swf Störungstheorie (DE-588)4128420-3 gnd rswk-swf Matrizengleichung (DE-588)4169125-8 s Störungstheorie (DE-588)4128420-3 s DE-604 Konstantinov, Mihail Sonstige oth Studies in computational mathematics 9 (DE-604)BV001895633 9 http://www.loc.gov/catdir/enhancements/fy0614/2003053106-d.html HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018583151&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Perturbation theory for matrix equations Studies in computational mathematics Matrices Perturbation (Mathematics) Matrizengleichung (DE-588)4169125-8 gnd Störungstheorie (DE-588)4128420-3 gnd |
| subject_GND | (DE-588)4169125-8 (DE-588)4128420-3 |
| title | Perturbation theory for matrix equations |
| title_auth | Perturbation theory for matrix equations |
| title_exact_search | Perturbation theory for matrix equations |
| title_full | Perturbation theory for matrix equations Mihail Konstantinov ... |
| title_fullStr | Perturbation theory for matrix equations Mihail Konstantinov ... |
| title_full_unstemmed | Perturbation theory for matrix equations Mihail Konstantinov ... |
| title_short | Perturbation theory for matrix equations |
| title_sort | perturbation theory for matrix equations |
| topic | Matrices Perturbation (Mathematics) Matrizengleichung (DE-588)4169125-8 gnd Störungstheorie (DE-588)4128420-3 gnd |
| topic_facet | Matrices Perturbation (Mathematics) Matrizengleichung Störungstheorie |
| url | http://www.loc.gov/catdir/enhancements/fy0614/2003053106-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018583151&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001895633 |
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