Antoulas A.C. — Approximation of Large-Scale Dynamical Systems :: Электронная библиотека попечительского совета мехмата МГУ

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Antoulas A.C. — Approximation of Large-Scale Dynamical Systems

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Название: Approximation of Large-Scale Dynamical Systems

Автор: Antoulas A.C.

Аннотация:

SIAM's Advances in Design and Control series consists of texts and monographs dealing with all areas of design and control and their applications. Topics of interest include shape optimization, multidisciplinary design, trajectory optimization, feedback, and optimal control. The series focuses on the mathematical and computational aspects of engineering design and control that are usable in a wide variety of scientific and engineering disciplines.

Язык:

Рубрика: Технология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 479

Добавлена в каталог: 31.01.2010

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Предметный указатель

$h_{2}$ spaces      125
$h_{2}$ -norm      126
$h_{p}$ -norms      125
$h_{\infty}$ -norm      126
$\ell_{2}$ spaces, inner product      127
$\ell_{2}$ spaces, time domain      126
$\ell_{p}$ spaces      124
$\ell_{p}$ -norms      124
$\mathcal{H}_{2}$ , is this norm induced?      144
$\mathcal{H}_{2}$ -norm      126
$\mathcal{H}_{2}$ -norm and EVD      144
$\mathcal{H}_{2}$ -norm and gramians      144
$\mathcal{H}_{2}$ -norm of system      144
$\mathcal{H}_{2}$ -norm, discrete-time systems      146
$\mathcal{H}_{p}$ spaces      126
$\mathcal{H}_{p}$ -norms      125
$\mathcal{H}_{\infty}$ -norm      126
$\mathcal{H}_{\infty}$ -norm bisection algorithm      133
$\mathcal{H}_{\infty}$ -norm of convolution operator      132
$\mathcal{L}_{2}$ spaces, inner product      127
$\mathcal{L}_{2}$ spaces, time domain      126
$\mathcal{L}_{2}$ -norm of impulse response      144
$\mathcal{L}_{p}$ spaces      124
$\mathcal{L}_{p}$ spaces, frequency domain      126
$\mathcal{L}_{p}$ -norms      124
$\mathcal{L}_{p}$ -norms, frequency domain      126
AAK (Adamjan — Arov — Krein) theorem      252
Algorithms, approximate balancing algorithm      375
Algorithms, approximate balancing algorithm, MIMO case      377
Algorithms, case studies      389
Algorithms, case studies, aluminum plate      410
Algorithms, case studies, building model      392
Algorithms, case studies, Butterworth filter      398
Algorithms, case studies, CD player      394
Algorithms, case studies, CD player-Smith algorithms      406
Algorithms, case studies, clamped beam model      396
Algorithms, case studies, heat diffusion model      394
Algorithms, case studies, heat distribution n = 20,736      410
Algorithms, case studies, image approximation      389
Algorithms, case studies, ISS stage 12A      403
Algorithms, case studies, ISS stage 1R      400
Algorithms, case studies, system of order n = 1000      408
Algorithms, complexity of      415
Algorithms, Lanczos and Arnoldi      334
Algorithms, parallelization      4
Algorithms, polynomial time      4
Algorithms, randomized      4
Algorithms, Smith methods      380 381
Algorithms, Smith methods, ADI iteration      381
Algorithms, Smith methods, cyclic Smith(l)      382
Algorithms, Smith methods, low rank ADI and cyclic Smith      382
Algorithms, Smith methods, modified low rank Smith(l)      384
Algorithms, Smith methods, trapezoidal rule, and      387
Algorithms, software      415
Alternating direction implicit (ADI)      380
Approximation by balanced truncation      207
Approximation by balanced truncation, $\mathcal{H}_{2}$ error norm      218
Approximation by balanced truncation, additive error bound      213 215
Approximation by balanced truncation, bounded real balancing      231
Approximation by balanced truncation, canonical form      224
Approximation by balanced truncation, continuous-time      213
Approximation by balanced truncation, continuous/discrete systems      211
Approximation by balanced truncation, discrete-time      215
Approximation by balanced truncation, four algorithms      220
Approximation by balanced truncation, frequency weighted balancing      235 237
Approximation by balanced truncation, frequency weighted balancing (gramians)      236 239
Approximation by balanced truncation, Lyapunov balancing      229
Approximation by balanced truncation, positive real balancing      232
Approximation by balanced truncation, positive real balancing, error bound      234
Approximation by balanced truncation, proof of error bound      216
Approximation by balanced truncation, stochastic balancing      229
Approximation by balanced truncation, stochastic balancing, multiplicative error bound      230
Approximation by balanced truncation, time-limited balancing      241
Approximation by balanced truncation, types of balancing      228
Approximation by balanced truncation, unstable systems      242
Approximation by balanced truncation, weighted balancing and Krylov      366
Approximation by Hankel-norm approximation      249
Approximation, algorithms, complexity of      415
Approximation, algorithms, software      415
Approximation, Arnoldi and moment matching      348
Approximation, Arnoldi and moment matching, Hessenberg form      349
Approximation, case studies      389
Approximation, eigenvalues of gramians, decay rate bound      293
Approximation, eigenvalues of gramians, decay rate estimate      291
Approximation, exercises      421
Approximation, Hankel singular values, Cauchy kernel      288
Approximation, Hankel singular values, Cauchy matrices      287
Approximation, Hankel singular values, decay rate      285 294
Approximation, Hankel singular values, decay rate, numerical examples      298
Approximation, Hankel-norm approximation, AAK theorem      252
Approximation, Hankel-norm approximation, all suboptimal solutions      259
Approximation, Hankel-norm approximation, construction of approximants      254
Approximation, Hankel-norm approximation, error bounds      262
Approximation, Hankel-norm approximation, input-output construction of approximants      254
Approximation, Hankel-norm approximation, main ingredients      250
Approximation, Hankel-norm approximation, main result      252
Approximation, Hankel-norm approximation, polynomial approach      267
Approximation, Hankel-norm approximation, unitary dilation      256
Approximation, Hankel-norm approximation, unitary dilation, optimal case      258
Approximation, Hankel-norm approximation, unitary dilation, suboptimal case      258
Approximation, Krylov methods      343
Approximation, Krylov methods, generality of rational Krylov      357
Approximation, Krylov methods, preservation of passivity      358
Approximation, Krylov methods, properties      350
Approximation, Lanczos and moment matching      346
Approximation, Lanczos and moment matching, error      349
Approximation, Lanczos and moment matching, tridiagonal form      347
Approximation, methods      10
Approximation, modal approximation      282
Approximation, moment matching      346
Approximation, moments of a function      345
Approximation, open problems      416
Approximation, projection, by      8
Approximation, projectors, summary      413
Approximation, proper orthogonal decomposition (POD)      277
Approximation, proper orthogonal decomposition (POD), adjoint system      281
Approximation, proper orthogonal decomposition (POD), empirical eigenfunctions      278
Approximation, proper orthogonal decomposition (POD), Galerkin projection      279
Approximation, proper orthogonal decomposition (POD), Petrov — Galerkin projection      279
Approximation, proper orthogonal decomposition (POD), POD and balancing      279
Approximation, proper orthogonal decomposition (POD), snapshots      278 279 281
Approximation, special topics      277
Approximation, SVD-Krylov methods      365
Approximation, SVD-Krylov methods, approximation balancing algorithm      375 377
Approximation, SVD-Krylov methods, cross gramian      373
Approximation, SVD-Krylov methods, iterative approximation balanced reduction      371
Approximation, SVD-Krylov methods, iterative methods      371
Approximation, SVD-Krylov methods, Krylov and Sylvester equations      366
Approximation, SVD-Krylov methods, least squares approximation      368 370
Approximation, SVD-Krylov methods, Smith methods      380
Approximation, SVD-Krylov methods, weighted balancing and Krylov      366
Approximation, truncation and residualization      285
Arnoldi and FOM, CG, GMRES, MINRES      331
Arnoldi method, algorithm      334
Arnoldi method, alternative way of looking at      331
Arnoldi method, eigenvalue estimation      328
Arnoldi method, eigenvalue estimation, fundamental lemma      331
Arnoldi method, implicitly restarted Arnoldi      336
Arnoldi method, implicitly restarted Arnoldi, convergence      337
Arnoldi method, moment matching      348
Arnoldi method, moment matching, Hessenberg form      349
Arnoldi method, rational Arnoldi      336
Banach space      123
Behavioral framework      62
Bilinear transformation discrete continuous systems      87
Bisection algorithm for induced 2- or $\mathcal{H}_{\infty}$ -norm      133
Bounded real lemma      169
Bounded-input, bounded-output (BIBO)      151
case studies      389
Case studies, aluminum plate      410

Case studies, building model      392
Case studies, Butterworth filter      398
Case studies, CD player      394
Case studies, CD player, Smith algorithms      406
Case studies, clamped beam model      396
Case studies, heat diffusion model      394
Case studies, heat distribution n = 20,736      410
Case studies, image approximation      389
Case studies, ISS stage 12A      403
Case studies, ISS stage 1R      400
Case studies, system of order n = 1000      408
Cauchy kernel      288
Cauchy matrices      287
Cholesky decomposition      28
Cholesky decomposition, factors      411
Cholesky ordering      290
Circulant Toeplitz matrix      129
Condition number      42
Condition number, eigenvalues      44
Condition number, eigenvectors      44
Condition number, EVD and SVD      43
Condition number, linear system of equations      43
Condition number, matrix-vector product      43
Conjugate Gradient (CG)      331
Continued fraction decomposition      114
Controllability      73
Controllability, distance to      74
Convolution      59
Convolution operator      128
Convolution operator, $\mathcal{H}_{\infty}$ -norm      132
Convolution operator, 2-induced norm      132
Convolution operator, 2-induced or $\mathcal{H}_{\infty}$ -norm Hamiltonian      133
Convolution operator, adjoint of      131
Convolution operator, convolution sum      60
Convolution operator, resolvent      128
Convolution operator, singular values      128
Convolution operator, singular values (continuous-time)      130
Convolution operator, singular values MIMO systems      130
Convolution operator, spectrum      128
Convolution operator, spectrum (continuous-time)      130
Convolution operator, spectrum, MIMO systems      130
Convolution, periodic (discrete-time)      128
Convolution, sum (discrete-sum)      60
Cross gramian      85
Cross gramian, approximate balanced reduction      373
Cross gramian, approximate balancing algorithm      375
Cross gramian, approximate balancing algorithm, MIMO case      377
Cross gramian, eigenvalues of Hankel operator      137
Decay rates of Hankel singular values      285 294
Decay rates of Hankel singular values, Cauchy kernel      288
Decay rates of Hankel singular values, Cauchy matrices      287
Decay rates of Hankel singular values, Cholesky ordering      290
Decay rates of Hankel singular values, multiplicative majorization      294
Decay rates of Hankel singular values, numerical examples      298
Decompositions rank additive      52
Derivative operator      59
Detectability      77
Dissipative systems      159
Dissipative systems, available storage      159
Dissipative systems, bounded real lemma      169
Dissipative systems, dissipation inequality      159
Dissipative systems, linear system, quadratic supply      160
Dissipative systems, LMI      161
Dissipative systems, positive real lemma      163
Dissipative systems, required supply      159
Dissipative systems, Riccati equation      161
Dissipative systems, storage and Lyapunov functions      159
Dissipative systems, storage function      159
Dissipative systems, supply function      159
Distance to singularity      50
Distance to unobservability      78
Distance to unreachability      74
Duality of linear systems      76
Dynamical systems      63
Eigenvalue computations      313
Eigenvalue computations, basic Krylov iteration      313
Eigenvalue decomposition (EVD)      36 314
Eigenvalue decomposition (EVD), Bauer — Fike result      316
Eigenvalue decomposition (EVD), characteristic polynomial      315
Eigenvalue decomposition (EVD), condition numbers      315
Eigenvalue decomposition (EVD), eigenvalue estimation, Arnoldi method      328
Eigenvalue decomposition (EVD), eigenvalue estimation, iterative methods      320
Eigenvalue decomposition (EVD), eigenvalue estimation, iterative methods, inverse vector iteration      322
Eigenvalue decomposition (EVD), eigenvalue estimation, iterative methods, Rayleigh quotient      323
Eigenvalue decomposition (EVD), eigenvalue estimation, iterative methods, Rayleigh — Ritz procedure      321
Eigenvalue decomposition (EVD), eigenvalue estimation, iterative methods, subspace iteration      323
Eigenvalue decomposition (EVD), eigenvalue estimation, iterative methods, vector iteration      322
Eigenvalue decomposition (EVD), eigenvalue estimation, Krylov methods      324
Eigenvalue decomposition (EVD), eigenvalue estimation, Lanczos method      325
Eigenvalue decomposition (EVD), eigenvalues, algebraic/geometric multiplicity      315
Eigenvalue decomposition (EVD), eigenvalues, condition number      318
Eigenvalue decomposition (EVD), eigenvalues/eigenvectors      314
Eigenvalue decomposition (EVD), Jordan blocks      315
Eigenvalue decomposition (EVD), perturbation of eigenvalues/eigenvectors      317
Eigenvalue decomposition (EVD), pseudospectra      318
Eigenvalue estimation, iterative methods      320
Eigenvalue estimation, iterative methods, Arnoldi method      328
Eigenvalue estimation, iterative methods, inverse vector iteration      322
Eigenvalue estimation, iterative methods, Krylov methods      324
Eigenvalue estimation, iterative methods, Lanczos method      325
Eigenvalue estimation, iterative methods, Rayleigh quotient      323
Eigenvalue estimation, iterative methods, Rayleigh — Ritz procedure      321
Eigenvalue estimation, iterative methods, subspace iteration      323
Eigenvalue estimation, iterative methods, vector iteration      322
exercises      421
External description      59
External description, Markov parameters      66
Feedback interpretation, recursive interpolation      114
Finite gramian      79
Floating point arithmetic      44
Floating point arithmetic, ANSI/IEEE arithmetic      45
Fourier transform      127
Fourier transform, Parseval, Plancherel, Paley — Wiener relationships      127
Full Orthogonalization Method (FOM)      331
Galerkin projection      277 279—281
Generalized minimal residual method (GMRES)      331
Generalized observability matrix      102
Generalized reachability matrix      102
Gramians for weighted systems      236
Gramians, Cholesky ordering      290
Gramians, closed-loop gramians      241
Gramians, cross      85
Gramians, cross, approximate balanced reduction      373
Gramians, cross, approximate balancing algorithm      375
Gramians, cross, approximate balancing algorithm (MIMO case)      377
Gramians, cross, eigenvalues of Hankel operator      137
Gramians, decay rate bound of eigenvalues      293
Gramians, decay rate estimate of eigenvalues      291
Gramians, frequency weighted without weights      239
Gramians, Hankel singular values (continuous-time)      139
Gramians, Hankel singular values (discrete-time)      138
Gramians, infinite      78
Gramians, infinite, in frequency      80
Gramians, time-limited gramians      241
Hamiltonian for 2-induced or $\mathcal{H}_{\infty}$ -norm      133
Hamiltonian for passive model reduction      359
Hankel matrix      90
Hankel matrix, factorization      91
Hankel matrix, Hankel operator and      136
Hankel matrix, partially defined      98
Hankel operator, continuous-time      135
Hankel operator, discrete-time      135
Hankel operator, eigenvalues of      137
Hankel operator, eigenvalues of, cross gramian      137
Hankel operator, Hankel matrix and      136
Hankel operator, Hilbert — Schmidt norm      141
Hankel operator, norm      135
Hankel operator, singular values      138
Hankel operator, singular values, continuous-time      139
Hankel operator, singular values, discrete-time case      138

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