|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Antoulas A.C. — Approximation of Large-Scale Dynamical Systems |
|
|
|
| Предметный указатель |
Hankel singular values (HSV) 138
Hankel singular values (HSV), assignment of 307
Hankel singular values (HSV), continuous-time 139
Hankel singular values (HSV), cross gramian and 140
Hankel singular values (HSV), decay rates 285 294
Hankel singular values (HSV), decay rates, Cauchy kernel 288
Hankel singular values (HSV), decay rates, Cauchy matrices 287
Hankel singular values (HSV), decay rates, multiplicative majorization 294
Hankel singular values (HSV), decay rates, numerical examples 298
Hankel singular values (HSV), discrete-time case 138
Hankel singular values (HSV), lemma 139
Hankel-norm approximation 249
Hankel-norm approximation, AAK theorem 252
Hankel-norm approximation, all suboptimal solutions 259
Hankel-norm approximation, construction of approximants 254
Hankel-norm approximation, error bounds 262
Hankel-norm approximation, Hankel operator, eigenvalue equation 270
Hankel-norm approximation, Hankel operator, Schmidt pairs 269
Hankel-norm approximation, input-output construction of approximants 254
Hankel-norm approximation, main ingredients 250
Hankel-norm approximation, main result 252
Hankel-norm approximation, polynomial approach 267
Hankel-norm approximation, polynomial approach, balanced canonical form 273
Hankel-norm approximation, polynomial approach, error formulae 275
Hankel-norm approximation, polynomial approach, Hankel operator and SVD 268
Hankel-norm approximation, polynomial approach, Nehari problem 272
Hankel-norm approximation, unitary dilation 256
Hankel-norm approximation, unitary dilation, optimal case 258
Hankel-norm approximation, unitary dilation, suboptimal case 258
Hardy norms, frequency domain 149
Hilbert space 123
Hilbert — Schmidt norm 141
Hilbert — Schmidt operator 141
Homework assignments 421—439
Implicitly restarted Arnoldi method (IRAM) 336
Implicitly restarted Arnoldi method (IRAM), convergence 337
Impulse  62
Impulse response 65
Induced 2-norm of convolution operator 132
Induced 2-norm, bisection algorithm 133
Induced norms and noninduced norms of convolution operator 150
Induced norms, convolution, Hankel operators 147
Induced norms, convolution, Hankel operators, (p,q) Lebesgue spaces 147
Induced norms, convolution, Hankel operators, (p,q) norms 148
Induced norms, convolution, Hankel operators, equi-induced norms 148
Induced norms, convolution, Hankel operators, mixed-induced norms 148
Induced norms, convolution, Hankel operators, spatial norm 147
Induced norms, convolution, Hankel operators, temporal norm 147
Inertia, definition 188
Inertia, iterative proof of 195
Inertia, Lyapunov equations, and 188
Inertia, Sylvester law of 189
Input 59
Input energy 71
Interlacing 53
Internal description 59 63
International Space Station (ISS) 20
Iterative approximation, approximate balanced reduction 371
Iterative approximation, approximate balanced reduction, algorithm 375 377
Iterative approximation, approximate balanced reduction, cross gramian and 373
Iterative approximation, Smith methods 380 381
Iterative approximation, Smith methods, ADI iteration 381
Iterative approximation, Smith methods, cyclic Smith(l) 382
Iterative approximation, Smith methods, low rank ADI and cyclic Smith 382
Iterative approximation, Smith methods, modified low rank Smith(l) 384
Iterative approximation, Smith methods, trapezoidal rule, and 387
Iterative approximation, SVD-Krylov methods 371
Kernel (weighting pattern) 61
Krylov methods, eigenvalue estimation 324
Krylov methods, eigenvalue estimation, Arnoldi method 328
Krylov methods, eigenvalue estimation, convergence of Lanczos method 326
Krylov methods, eigenvalue estimation, Lanczos method 325
Krylov methods, eigenvalue estimation, motivation 324
Krylov methods, generality of rational Krylov 357
Krylov methods, implicitly restarted Arnoldi method 336
Krylov methods, Krylov subspace 68
Krylov methods, Krylov, basic iteration 313
Krylov methods, preservation of passivity 358
Krylov methods, rational Arnoldi method 336
Krylov methods, rational Krylov methods 335
Lagrange polynomial 100
Lanczos method, algorithm 334
Lanczos method, eigenvalue estimation 325
Lanczos method, eigenvalue estimation, convergence of 326
Lanczos method, moment matching 346
Lanczos method, moment matching, continued fractions 351
Lanczos method, moment matching, error 349
Lanczos method, moment matching, tridiagonal form 347
Lanczos method, properties 332
Lanczos method, three-term recurrence 332
Lanczos method, two-sided Lanczos 333
LAPACK software 51
Laplace transform 62
Laurent operator 60 128
Least squares problem 40 53
Least squares system approximation 368
Least squares system approximation, moment matching 370
Least squares system approximation, Prony's method 370
Lebesgue norms, frequency domain 149
Lebesgue spaces, time domain 124
Linear matrix inequality (LMI), dissipative systems 161
Loewner matrix 99 102
LU decomposition 28 323 336 347 355
Lyapunov and Sylvester equations 173
Lyapunov and Sylvester equations in Schur basis 191
Lyapunov and Sylvester equations, algorithms 200
Lyapunov and Sylvester equations, Bartels — Stewart algorithm 191
Lyapunov and Sylvester equations, characteristic polynomial methods 179
Lyapunov and Sylvester equations, complex integration method 176
Lyapunov and Sylvester equations, eigenvalue/eigenvector method 178
Lyapunov and Sylvester equations, eigenvalue/eigenvector method, generalized, reachability/observability, matrices 179
Lyapunov and Sylvester equations, Hammarling algorithm 196
Lyapunov and Sylvester equations, inertia 188
Lyapunov and Sylvester equations, invariant subspace method 184
Lyapunov and Sylvester equations, Kronecker product method 175
Lyapunov and Sylvester equations, numerical issues, condition number of solutions 203
Lyapunov and Sylvester equations, numerical issues, forward/backward stability 201
Lyapunov and Sylvester equations, sign function method 184
Lyapunov and Sylvester equations, square root method 196
Lyapunov and Sylvester equations, triangular coefficients 191
Lyapunov equation, continuous-time 78
Lyapunov equation, discrete-time (Stein) 79
Lyapunov equation, Schur basis 193
Lyapunov equation, Schur basis, iterative proof of inertia 195
Lyapunov equation, sign function, and the 184
Majorization and interlacing 53
Markov parameters 62 66
Matrix exponential 64
Matrix exponential, formula 70
Matrix theory 27
Matrix theory, big six matrix decompositions 28
Matrix theory, Cholesky decomposition 28
Matrix theory, eigenvalue computations 313
Matrix theory, Jordan blocks 315
Matrix theory, LU decomposition 28 323 336 347 355
Matrix theory, norms of vectors and matrices 28
Matrix theory, QR decomposition 28 314 321 324 332 337 348
Matrix theory, Schur decomposition 28 320 323
McMillan degree 96 100
Minimal residual method (MINRES) 331
Modal approximation 282
Model reduction by balanced truncation 207
Model reduction by balanced truncation,  error norm 218
Model reduction by balanced truncation, additive error bound 213 215
Model reduction by balanced truncation, bounded real balancing 231
Model reduction by balanced truncation, canonical form 224
Model reduction by balanced truncation, continuous-time 213
Model reduction by balanced truncation, continuous/discrete systems 211
Model reduction by balanced truncation, discrete-time 215
Model reduction by balanced truncation, four algorithms 220
| Model reduction by balanced truncation, frequency weighted balancing 235 237
Model reduction by balanced truncation, frequency weighted balancing (gramians) 236 239
Model reduction by balanced truncation, Lyapunov balancing 229
Model reduction by balanced truncation, positive real balancing 232
Model reduction by balanced truncation, positive real balancing, error bound 234
Model reduction by balanced truncation, proof of error bound 216
Model reduction by balanced truncation, stochastic balancing 229
Model reduction by balanced truncation, stochastic balancing, multiplicative error bound 230
Model reduction by balanced truncation, time-limited balancing 241
Model reduction by balanced truncation, types of balancing 228
Model reduction by balanced truncation, unstable systems 242
Model reduction by balanced truncation, weighted balancing and Krylov 366
Model reduction by Hankel-norm approximation 249
Model reduction, algorithms, complexity of 415
Model reduction, algorithms, software 415
Model reduction, Arnoldi and moment matching 348
Model reduction, Arnoldi and moment matching, Hessenberg form 349
Model reduction, case studies 389
Model reduction, eigenvalues of gramians, decay rate bound 293
Model reduction, eigenvalues of gramians, decay rate estimate 291
Model reduction, exercises 421
Model reduction, Hankel singular values, Cauchy kernel 288
Model reduction, Hankel singular values, Cauchy matrices 287
Model reduction, Hankel singular values, decay rate 285 294
Model reduction, Hankel singular values, decay rate, numerical examples 298
Model reduction, Hankel-norm approximation, AAK theorem 252
Model reduction, Hankel-norm approximation, all suboptimal solutions 259
Model reduction, Hankel-norm approximation, construction of approximants 254
Model reduction, Hankel-norm approximation, error bounds 262
Model reduction, Hankel-norm approximation, input-output construction of approximants 254
Model reduction, Hankel-norm approximation, main ingredients 250
Model reduction, Hankel-norm approximation, main result 252
Model reduction, Hankel-norm approximation, polynomial approach 267
Model reduction, Hankel-norm approximation, unitary dilation 256
Model reduction, Hankel-norm approximation, unitary dilation, optimal case 258
Model reduction, Hankel-norm approximation, unitary dilation, suboptimal case 258
Model reduction, Krylov methods 343
Model reduction, Krylov methods, generality of rational Krylov 357
Model reduction, Krylov methods, preservation of passivity 358
Model reduction, Krylov methods, properties 350
Model reduction, Lanczos and moment matching 346
Model reduction, Lanczos and moment matching, error 349
Model reduction, Lanczos and moment matching, tridiagonal form 347
Model reduction, modal approximation 282
Model reduction, moment matching 346
Model reduction, moments of a function 345
Model reduction, open problems 416
Model reduction, projectors, summary 413
Model reduction, proper orthogonal decomposition (POD) 277
Model reduction, proper orthogonal decomposition (POD), adjoint system 281
Model reduction, proper orthogonal decomposition (POD), empirical eigenfunctions 278
Model reduction, proper orthogonal decomposition (POD), Galerkin projection 279
Model reduction, proper orthogonal decomposition (POD), Petrov — Galerkin projection 279
Model reduction, proper orthogonal decomposition (POD), POD and balancing 279
Model reduction, proper orthogonal decomposition (POD), snapshots 278 279 281
Model reduction, special topics 277
Model reduction, SVD-Krylov methods 365
Model reduction, SVD-Krylov methods, approximation balancing algorithm 375 377
Model reduction, SVD-Krylov methods, cross gramian 373
Model reduction, SVD-Krylov methods, iterative approximate balanced reduction 371
Model reduction, SVD-Krylov methods, iterative methods 371
Model reduction, SVD-Krylov methods, Krylov and Sylvester equations 366
Model reduction, SVD-Krylov methods, least squares approximation 368 370
Model reduction, SVD-Krylov methods, Smith methods 380
Model reduction, SVD-Krylov methods, weighted balancing and Krylov 366
Model reduction, truncation and residualization 285
Moment matching 346
Moments of a function 345
Moore — Penrose pseudoinverse 40
Multi-input, multi-output (MIMO) 60
Network synthesis 169
Nevanlinna — Pick problem 100
Nevanlinna — Pick problem, algebraization of 117
Normed spaces 123
Normed spaces, Banach space 123
Normed spaces, Cauchy sequence 123
Normed spaces, convergence 123
Normed spaces, Hilbert space 123
Normed spaces, inner prduct 124
Normed spaces, maximum modulus theorem 126
Normed spaces, orthogonal complement 124
Norms, Cauchy — Schwarz inequality 29
Norms, definition of 28
Norms, equi-induced 148
Norms, equi-induced norms 30
Norms, Hilbert — Schmidt 141
Norms, Hoelder inequality 29
Norms, matrix induced norms 30
Norms, mixed-induced 148
Norms, noninduced and induced of convolution operator 150
Norms, p-norms of vectors 29
Norms, Schatten matrix norms 30
Norms, spatial 147
Norms, submultiplicativity of matrix norms 31
Norms, temporal 147
Norms, unit balls 29
Norms, unstable system 154
Norms, vectors and matrices 28
Notation xxiv
Numerical analysis 41
Numerical analysis, accuracy of numerical result 48
Numerical analysis, condition numbers 42
Numerical analysis, distance to singularity 50
Numerical analysis, floating point arithmetic 44
Numerical analysis, ill-posedness of rank 49
Numerical analysis, LAPACK software 51
Numerical analysis, Lyapunov equation, condition number of solutions 203
Numerical analysis, Lyapunov equation, forward/backward stability 201
Numerical analysis, numerical rank 50
Numerical analysis, stability of algorithms 44
Numerical analysis, stability of algorithms, backward error 44
Numerical analysis, stability of algorithms, forward error 44
Numerical analysis, stability of SVD 49
Numerical rank 50
Nyquist plot, Hilbert — Schmidt norm 141
Nyquist plot, spectrum of convolution operator 128 130
Observability 75
Observability, degree of 80
Observability, distance to unobservability 78
Observability, generalized observability matrix 102 179
Observability, gramian (finite) 76
Observability, infinite gramians 78
Observability, observability conditions 78
Observability, observability gramian 76
Observability, observability matrix 75
Observability, observable decomposition 77
Observability, observable subsystem 77
Observability, reachable-observable decomposition 77
Observability, unobservable state 75
Observability, unobservable subspace 75
Open problems in model reduction 416
Output 59
Output equations 63
Partial realization 97
Periodic convolution 128
Petrov — Galerkin condition 315
Petrov — Galerkin projection 277 279 281
Polynomial time algorithms 4
Popov — Belevich — Hautus (PHB) test 72
Positive real lemma 163
Problems, open in model reduction 416
Prony's method and least squares system approximation 370
Proper orthogonal decomposition (POD) 277
Proper orthogonal decomposition (POD), adjoint system 281
Proper orthogonal decomposition (POD), autocorrelation 278
Proper orthogonal decomposition (POD), empirical eigenfunctions 278
Proper orthogonal decomposition (POD), Galerkin projection 279
Proper orthogonal decomposition (POD), gramian 278
Proper orthogonal decomposition (POD), Petrov — Galerkin projection 279
Proper orthogonal decomposition (POD), POD and balancing 279
|
|
|
| Реклама |
|
|
|
|
|
|
|
|
О проекте