Approximation of large-scale dynamical systems:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia
SIAM Society for Industrial and Applied Mathematics
2005
|
| Series: | Advances in design and control
6 |
| Subjects: | |
| Online Access: | Publisher description Table of contents only Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | xxv, 479 Seiten Illustrationen, Diagramme |
| ISBN: | 0898715296 9780898716580 |
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MARC
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| 100 | 1 | |a Antoulas, Athanasios C. |d 1950- |0 (DE-588)112801889 |4 aut | |
| 245 | 1 | 0 | |a Approximation of large-scale dynamical systems |c Athanasios C. Antoulas |
| 264 | 1 | |a Philadelphia |b SIAM Society for Industrial and Applied Mathematics |c 2005 | |
| 300 | |a xxv, 479 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Advances in design and control |v 6 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Differential equations, Partial | |
| 650 | 4 | |a System analysis | |
| 650 | 4 | |a Approximation theory | |
| 650 | 4 | |a Linear systems | |
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Record in the Search Index
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| adam_text | APPROXIMATION OF LARGE-SCALE DYNAMICAL SYSTEMS ATHANASIOS C. ANTOULAS
RICE UNIVERSITY HOUSTON.TEXAS SOCIETY FOR INDUSTRIAL AND APPLIED
MATHEMATICS PHILADELPHIA CONTENTS LIST OF FIGURES XIII FOREWORD XVII
PREFACE XIX HOW TO USE THIS BOOK XXIII I INTRODUCTION 1 1 INTRODUCTION 3
1.1 PROBLEM SET-UP 5 1.1.1 APPROXIMATION BY PROJECTION 8 1.2 SUMMARY OF
CONTENTS 10 2 MOTIVATING EXAMPLES 11 2.1 PASSIVE DEVICES 11 2.2 WEATHER
PREDICTION*DATA ASSIMILATION 13 2.2.1 NORTH SEA WAVE SURGE FORECAST 13
2.2.2 PACIFIC STORM TRACKING 15 2.2.3 AMERICA S CUP 16 2.3 AIR QUALITY
SIMULATIONS*DATA ASSIMILATION 16 2.4 BIOLOGICAL SYSTEMS: HONEYCOMB
VIBRATIONS 17 2.5 MOLECULAR DYNAMICS 18 2.6 INTERNATIONAL SPACE STATION
20 2.7 VIBRATION/ACOUSTIC SYSTEMS 20 2.8 CVD REACTORS 21 2.9
MICROELECTROMECHANICAL DEVICES 21 2.9.1 MICROMIRRORS 22 2.9.2 ELK SENSOR
22 2.10 OPTIMAL COOLING OF STEEL PROFILE 24 II PRELIMINARIES 25 3 TOOLS
FROM MATRIX THEORY 27 3.1 NORMS OF FINITE-DIMENSIONAL VECTORS AND
MATRICES 28 VII VIII CONTENTS 3.2 THE SVD 31 3.2.1 THREE PROOFS 33 3.2.2
PROPERTIES OF THE SVD 35 3.2.3 COMPARISON WITH THE EIGENVALUE
DECOMPOSITION 36 3.2.4 OPTIMAL APPROXIMATION IN THE 2-INDUCED NORM 37
3.2.5 FURTHER APPLICATIONS OF THE SVD 40 3.2.6 THE SEMIDISCRETE
DECOMPOSITION 41 3.3 BASIC NUMERICAL ANALYSIS 41 3.3.1 CONDITION NUMBERS
42 3.3.2 STABILITY OF SOLUTION ALGORITHMS 44 3.3.3 TWO CONSEQUENCES 49
3.3.4 DISTANCE TO SINGULARITY 50 3.3.5 LAPACK SOFTWARE 51 3.4 GENERAL
RANK ADDITIVE MATRIX DECOMPOSITIONS* 52 3.5 MAJORIZATION AND
INTERLACING* 53 3.6 CHAPTER SUMMARY 57 4 LINEAR DYNAMICAL SYSTEMS: PART
1 59 4.1 EXTERNAL DESCRIPTION 60 4.2 INTERNAL DESCRIPTION 63 4.2.1 THE
CONCEPT OF REACHABILITY 67 4.2.2 THE STATE OBSERVATION PROBLEM 74 4.2.3
THE DUALITY PRINCIPLE IN LINEAR SYSTEMS 76 4.3 THE INFINITE GRAMIANS 78
4.3.1 THE ENERGY ASSOCIATED WITH REACHING/OBSERVING A STATE 80 4.3.2 THE
CROSS GRAMIAN 85 4.3.3 A TRANSFORMATION BETWEEN CONTINUOUS- AND
DISCRETE-TIME SYSTEMS . 87 4.4 THE REALIZATION PROBLEM 88 4.4.1 THE
SOLUTION OF THE REALIZATION PROBLEM 91 4.4.2 REALIZATION OF PROPER
RATIONAL MATRIX FUNCTIONS 95 4.4.3 SYMMETRIC SYSTEMS AND SYMMETRIC
REALIZATIONS 96 4.4.4 THE PARTIAL REALIZATION PROBLEM 97 4.5 THE
RATIONAL INTERPOLATION PROBLEM* 99 4.5.1 PROBLEM FORMULATION* 99 4.5.2
THE LOWNER MATRIX APPROACH TO RATIONAL INTERPOLATION* 101 4.5.3
GENERATING SYSTEM APPROACH TO RATIONAL INTERPOLATION* 107 4.6 CHAPTER
SUMMARY 121 5 LINEAR DYNAMICAL SYSTEMS: PART 2 123 5.1 TIME AND
FREQUENCY DOMAIN SPACES AND NORMS 123 5.1.1 BANACH AND HILBERT SPACES
123 5.1.2 THE LEBESGUE SPACES I P AND C P 124 5.1.3 THE HARDY SPACES H P
AND H P 125 5.1.4 THE HILBERT SPACES 2 AND 2 126 5.2 THE SPECTRUM
AND SINGULAR VALUES OF THE CONVOLUTION OPERATOR 128 5.3 COMPUTATION OF
THE 2-INDUCED OR HOC -NORM 132 5.4 THE HANKEL OPERATOR AND ITS SPECTRA
134 5.4.1 COMPUTATION OF THE EIGENVALUES OF U 136 5.4.2 COMPUTATION OF
THE SINGULAR VALUES OF U 137 5.4.3 THE HILBERT-SCHMIDT NORM 141 CONTENTS
IX 5.4.4 THE HANKEL SINGULAR VALUES OF TWO RELATED OPERATORS 142 5.5
THE^-NORM 144 5.5.1 A FORMULA BASED ON THE GRAMIANS 144 5.5.2 A FORMULA
BASED ON THE EVD OF A 144 5.6 FURTHER INDUCED NORMS OF M* 147 5.7
SUMMARY OF NORMS 149 5.8 SYSTEM STABILITY 150 5.8.1 REVIEW OF SYSTEM
STABILITY 150 5.8.2 LYAPUNOV STABILITY 152 5.8.3 /^-SYSTEMS AND NORMS OF
UNSTABLE SYSTEMS 154 5.9 SYSTEM DISSIPATIVITY* 159 5.9.1 PASSIVITY AND
THE POSITIVE REAL LEMMA* 163 5.9.2 CONTRACTIVITY AND THE BOUNDED REAL
LEMMA* 169 5.10 CHAPTER SUMMARY 171 6 SYLVESTER AND LYAPUNOV EQUATIONS
173 6.1 THE SYLVESTER EQUATION 173 6.1.1 THE KRONECKER PRODUCT METHOD
175 6.1.2 THE EIGENVALUE/COMPLEX INTEGRATION METHOD 176 6.1.3 THE
EIGENVALUE/EIGENVECTOR METHOD 178 6.1.4 CHARACTERISTIC POLYNOMIAL
METHODS 179 6.1.5 THE INVARIANT SUBSPACE METHOD 184 6.1.6 THE SIGN
FUNCTION METHOD 184 6.1.7 SOLUTION AS AN INFINITE SUM 188 6.2 THE
LYAPUNOV EQUATION AND INERTIA 188 6.3 SYLVESTER AND LYAPUNOV EQUATIONS
WITH TRIANGULAR COEFFICIENTS 191 6.3.1 THE BARTELS-STEWART ALGORITHM 191
6.3.2 THE LYAPUNOV EQUATION IN THE SCHUR BASIS 193 6.3.3 THE SQUARE ROOT
METHOD FOR THE LYAPUNOV EQUATION 196 6.3.4 ALGORITHMS FOR SYLVESTER AND
LYAPUNOV EQUATIONS 200 6.4 NUMERICAL ISSUES: FORWARD AND BACKWARD
STABILITY* 201 6.5 CHAPTER SUMMARY 204 III SVD-BASED APPROXIMATION
METHODS 205 7 BALANCING AND BALANCED APPROXIMATIONS 207 7.1 THE CONCEPT
OF BALANCING 208 7.2 MODEL REDUCTION BY BALANCED TRUNCATION 211 7.2.1
PROOF OF THE TWO THEOREMS 213 7.2.2 T^-NORM OF THE ERROR SYSTEM FOR
BALANCED TRUNCATION 218 7.3 NUMERICAL ISSUES: FOUR ALGORITHMS 220 7.4 A
CANONICAL FORM FOR CONTINUOUS-TIME BALANCED SYSTEMS 224 7.5 OTHER TYPES
OF BALANCING* 228 7.5.1 LYAPUNOV BALANCING* 229 7.5.2 STOCHASTIC
BALANCING* 229 7.5.3 BOUNDED REAL BALANCING* 231 7.5.4 POSITIVE REAL
BALANCING* 232 7.6 FREQUENCY WEIGHTED BALANCED TRUNCATION* 235 7.6.1
FREQUENCY WEIGHTED BALANCED TRUNCATION* 237 CONTENTS 7.6.2 FREQUENCY
WEIGHTED BALANCED REDUCTION WITHOUT WEIGHTS* 239 7.6.3 BALANCED
REDUCTION USING TIME-LIMITED GRAMIANS* 241 7.6.4 CLOSED-LOOP GRAMIANS
AND MODEL REDUCTION* 241 7.6.5 BALANCING FOR UNSTABLE SYSTEMS* 242 7.7
CHAPTER SUMMARY 246 HANKEL-NORM APPROXIMATION 249 8.1 INTRODUCTION 249
8.1.1 MAIN INGREDIENTS 250 8.2 THE ADAMJAN-AROV-KREIN THEOREM 252 8.3
THE MAIN RESULT 252 8.4 CONSTRUCTION OF APPROXIMANTS 254 8.4.1 A SIMPLE
INPUT-OUTPUT CONSTRUCTION METHOD 254 8.4.2 AN ANALOGUE OF
SCHMIDT-ECKART-YOUNG-MIRSKY 256 8.4.3 UNITARY DILATION OF CONSTANT
MATRICES 256 8.4.4 UNITARY SYSTEM DILATION: SUBOPTIMAL CASE 258 8.4.5
UNITARY SYSTEM DILATION: OPTIMAL CASE 258 8.4.6 ALL SUBOPTIMAL SOLUTIONS
259 8.5 ERROR BOUNDS FOR OPTIMAL APPROXIMANTS 262 8.6 BALANCED AND
HANKEL-NORM APPROXIMATION: A POLYNOMIAL APPROACH* 267 8.6.1 THE HANKEL
OPERATOR AND ITS SVD* 268 8.6.2 THE NEHARI PROBLEM AND HANKEL-NORM
APPROXIMANTS* 272 8.6.3 BALANCED CANONICAL FORM* 273 8.6.4 ERROR
FORMULAS FOR BALANCED AND HANKEL-NORM APPROXIMATIONS* . . 275 8.7
CHAPTER SUMMARY 275 SPECIAL TOPICS IN SVD-BASED APPROXIMATION METHODS
277 9.1 PROPER ORTHOGONAL DECOMPOSITION 277 9.1.1 POD 278 9.1.2 GALERKIN
AND PETROV-GALERKIN PROJECTIONS 279 9.1.3 POD AND BALANCING 279 9.2
MODAL APPROXIMATION 282 9.3 TRUNCATION AND RESIDUALIZATION 285 9.4 A
STUDY OF THE DECAY RATES OF THE HANKEL SINGULAR VALUES* 285 9.4.1
PRELIMINARY REMARKS ON DECAY RATES* 286 9.4.2 CAUCHY MATRICES* 287 9.4.3
EIGENVALUE DECAY RATES FOR SYSTEM GRAMIANS* 288 9.4.4 DECAY RATE OF THE
HANKEL SINGULAR VALUES* 293 9.4.5 NUMERICAL EXAMPLES AND DISCUSSION* 298
9.5 ASSIGNMENT OF EIGENVALUES AND HANKEL SINGULAR VALUES* 307 9.6
CHAPTER SUMMARY ; 309 IV KRYLOV-BASED APPROXIMATION METHODS 311 10
EIGENVALUE COMPUTATIONS 313 10.1 INTRODUCTION 314 10.1.1 CONDITION
NUMBERS AND PERTURBATION RESULTS 315 10.2 PSEUDOSPECTRA* 318 10.3
ITERATIVE METHODS FOR EIGENVALUE ESTIMATION 320 CONTENTS XI 10.3.1 THE
RAYLEIGH-RITZ PROCEDURE 321 10.3.2 THE SIMPLE VECTOR ITERATION (POWER
METHOD) 322 10.3.3 THE INVERSE VECTOR ITERATION 322 10.3.4 RAYLEIGH
QUOTIENT ITERATION 323 10.3.5 SUBSPACE ITERATION 323 10.4 KRYLOV METHODS
324 10.4.1 A MOTIVATION FOR KRYLOV METHODS 324 10.4.2 THE LANCZOS METHOD
325 10.4.3 CONVERGENCE OF THE LANCZOS METHOD 326 10.4.4 THE ARNOLDI
METHOD 328 10.4.5 PROPERTIES OF THE ARNOLDI METHOD 329 10.4.6 AN
ALTERNATIVE WAY TO LOOK AT ARNOLDI 331 10.4.7 PROPERTIES OF THE LANCZOS
METHOD 332 10.4.8 TWO-SIDED LANCZOS 333 10.4.9 THE ARNOLDI AND LANCZOS
ALGORITHMS 334 10.4.10 RATIONAL KRYLOV METHODS 335 10.4.11 IMPLICITLY
RESTARTED ARNOLDI AND LANCZOS METHODS 336 10.5 CHAPTER SUMMARY 341 11
MODEL REDUCTION USING KRYLOV METHODS 343 11.1 THE MOMENTS OF A FUNCTION
345 11.2 APPROXIMATION BY MOMENT MATCHING 346 11.2.1 TWO-SIDED LANCZOS
AND MOMENT MATCHING 346 11.2.2 ARNOLDI AND MOMENT MATCHING 348 11.3
PARTIAL REALIZATION AND RATIONAL INTERPOLATION BY PROJECTION 353 11.3.1
TWO-SIDED PROJECTIONS 355 11.3.2 HOW GENERAL IS MODEL REDUCTION BY
RATIONAL KRYLOV? 357 11.3.3 MODEL REDUCTION WITH PRESERVATION OF
STABILITY AND PASSIVITY .... 358 11.4 CHAPTER SUMMARY 361 V SVD-KRYLOV
METHODS AND CASE STUDIES 363 12 SVD-KRYLOV METHODS 365 12.1 CONNECTION
BETWEEN SVD AND KRYLOV METHODS 365 12.1.1 KRYLOV METHODS AND THE
SYLVESTER EQUATION 366 12.1.2 FROM WEIGHTED BALANCING TO KRYLOV 366
12.1.3 APPROXIMATION BY LEAST SQUARES 368 12.2 INTRODUCTION TO ITERATIVE
METHODS 371 12.3 AN ITERATIVE METHOD FOR APPROXIMATE BALANCED REDUCTION
371 12.3.1 APPROXIMATE BALANCING THROUGH LOW RANK APPROXIMATION OF THE
CROSS GRAMIAN 373 12.4 ITERATIVE SMITH-TYPE METHODS FOR MODEL REDUCTION
380 12.4.1 ADI, SMITH, AND CYCLIC SMITH(/) ITERATIONS 380 12.4.2 LOW
RANK ADI AND LOW RANK SMITH(/) ITERATIONS 382 12.4.3 THE MODIFIED
LR-SMITH(Z) ITERATION 384 12.4.4 A DISCUSSION ON THE APPROXIMATELY
BALANCED REDUCED SYSTEM .... 386 12.4.5 RELATION OF THE SMITH METHOD TO
THE TRAPEZOIDAL RULE 387 12.5 CHAPTER SUMMARY 388 XII CONTENTS 13 CASE
STUDIES 389 13.1 APPROXIMATION OF IMAGES 389 13.2 MODEL REDUCTION
ALGORITHMS APPLIED TO LOW-ORDER SYSTEMS 390 13.2.1 BUILDING MODEL 392
13.2.2 HEAT DIFFUSION MODEL 394 13.2.3 THE CD PLAYER 394 13.2.4 CLAMPED
BEAM MODEL 396 13.2.5 LOW-PASS BUTTERWORTH FILTER 398 13.3 APPROXIMATION
OF THE ISS 1R AND 12A FLEX MODELS 399 13.3.1 STAGE 1R 400 13.3.2 STAGE
12A 403 13.4 ITERATIVE SMITH-TYPE METHODS 406 13.4.1 THE CD PLAYER 406
13.4.2 A SYSTEM OF ORDER N- 1006 408 13.4.3 ALUMINUM PLATE N = 3468 410
13.4.4 HEAT DISTRIBUTION ON A PLATE N = 20,736 410 14 EPILOGUE 413 14.1
PROJECTORS, COMPUTATIONAL COMPLEXITY, AND SOFTWARE 413 14.2 OPEN
PROBLEMS 416 15 PROBLEMS 421 BIBLIOGRAPHY 441 INDEX 467
|
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| author | Antoulas, Athanasios C. 1950- |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 540 |
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| ctrlnum | (OCoLC)634667160 (DE-599)BVBBV019857006 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV019857006 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:07:43Z |
| institution | BVB |
| isbn | 0898715296 9780898716580 |
| language | English |
| lccn | 2005046507 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013181583 |
| oclc_num | 634667160 |
| open_access_boolean | |
| owner | DE-20 DE-91G DE-BY-TUM DE-703 DE-29T DE-824 DE-706 DE-384 DE-83 DE-11 DE-188 DE-739 |
| owner_facet | DE-20 DE-91G DE-BY-TUM DE-703 DE-29T DE-824 DE-706 DE-384 DE-83 DE-11 DE-188 DE-739 |
| physical | xxv, 479 Seiten Illustrationen, Diagramme |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | SIAM Society for Industrial and Applied Mathematics |
| record_format | marc |
| series | Advances in design and control |
| series2 | Advances in design and control |
| spelling | Antoulas, Athanasios C. 1950- (DE-588)112801889 aut Approximation of large-scale dynamical systems Athanasios C. Antoulas Philadelphia SIAM Society for Industrial and Applied Mathematics 2005 xxv, 479 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Advances in design and control 6 Includes bibliographical references and index Differentiable dynamical systems Differential equations, Partial System analysis Approximation theory Linear systems Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 s Partielle Differentialgleichung (DE-588)4044779-0 s Approximationstheorie (DE-588)4120913-8 s DE-604 Advances in design and control 6 (DE-604)BV021715022 6 http://www.loc.gov/catdir/enhancements/fy0665/2005046507-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0665/2005046507-t.html Table of contents only GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013181583&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Antoulas, Athanasios C. 1950- Approximation of large-scale dynamical systems Advances in design and control Differentiable dynamical systems Differential equations, Partial System analysis Approximation theory Linear systems Approximationstheorie (DE-588)4120913-8 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4120913-8 (DE-588)4137931-7 (DE-588)4044779-0 |
| title | Approximation of large-scale dynamical systems |
| title_auth | Approximation of large-scale dynamical systems |
| title_exact_search | Approximation of large-scale dynamical systems |
| title_full | Approximation of large-scale dynamical systems Athanasios C. Antoulas |
| title_fullStr | Approximation of large-scale dynamical systems Athanasios C. Antoulas |
| title_full_unstemmed | Approximation of large-scale dynamical systems Athanasios C. Antoulas |
| title_short | Approximation of large-scale dynamical systems |
| title_sort | approximation of large scale dynamical systems |
| topic | Differentiable dynamical systems Differential equations, Partial System analysis Approximation theory Linear systems Approximationstheorie (DE-588)4120913-8 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Differentiable dynamical systems Differential equations, Partial System analysis Approximation theory Linear systems Approximationstheorie Differenzierbares dynamisches System Partielle Differentialgleichung |
| url | http://www.loc.gov/catdir/enhancements/fy0665/2005046507-d.html http://www.loc.gov/catdir/enhancements/fy0665/2005046507-t.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013181583&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV021715022 |
| work_keys_str_mv | AT antoulasathanasiosc approximationoflargescaledynamicalsystems |