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| Авторизация |
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| Antoulas A.C. — Approximation of Large-Scale Dynamical Systems |
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| Предметный указатель |
Proper orthogonal decomposition (POD), snapshots 278 279 281
Pseudospectra 318
QR decomposition 28 314 321 324 332 337 348
Quadrature and Smith methods 387
Rational Arnoldi method 336
Rational interpolation 99
Rational interpolation, bounded real solutions 100
Rational interpolation, complexity 100
Rational interpolation, constrained problems 100
Rational interpolation, construction of interpolants by complexity 105
Rational interpolation, feedback interpretation 111
Rational interpolation, generalizations 117
Rational interpolation, generating system approach 99 107
Rational interpolation, generating system approach, bounded real interpolation 116
Rational interpolation, generating system approach, interpolation by complexity 110
Rational interpolation, generating system approach, positive real interpolation 116
Rational interpolation, generating system approach, recursive solution 114
Rational interpolation, generating system approach, recursive solution, feedback interpretation 114
Rational interpolation, generating system approach, row reduced matrices 112
Rational interpolation, Lagrange polynomial 100
Rational interpolation, Loewner matrix 99 102
Rational interpolation, Loewner matrix approach 101
Rational interpolation, multiple points 107
Rational interpolation, Nevanlinna — Pick problem 100
Rational interpolation, Nevanlinna — Pick problem, algebraization of 117
Rational interpolation, polynomial exponential time series 108
Rational interpolation, positive real solutions 101
Rational interpolation, rational interpolation by projection 353
Rational interpolation, rational interpolation by projection, Sylvester equation 356
Rational interpolation, rational interpolation by projection, two-sided projections 354
Rational interpolation, realization and interpolation 107
Rational interpolation, realization and rational interpolation 109
Rational interpolation, recursive solution 114
Rational interpolation, shift 107
Rational interpolation, time series 107
Rational interpolation, unconstrained problem 100
Rational Krylov methods 335
Reachability 67
Reachability, degree of 80
Reachability, distance to 74
Reachability, distance to unreachability 74
Reachability, equivalent conditions 72
Reachability, generalized reachability matrix 102 179
Reachability, gramian (finite) 68
Reachability, infinite gramians 78
Reachability, input energy 71
Reachability, input norm 71
Reachability, matrix 67
Reachability, minimal energy input 71
Reachability, PHB test 72
Reachability, reachability gramian 68
Reachability, reachable subspace 67
Reachability, reachable subsystem 72
Reachability, reachable-observable decomposition 77
Reachability, subspace 68
Reachability, unreachable subsystem 72
Reachable canonical decomposition 71
Reachable-observable decomposition 77
Realization 88
Realization, minimal 93
Realization, partial Hankel matrix 98
Realization, partial realization 97
Realization, partial realization by projection 353
Realization, problem, solution of 91
Realization, proper rational matrices 95
Realization, realizable sequence 88
Realization, realization and interpolation 107
Realization, realization and rational interpolation 109
Realization, Silverman algorithm 92
Realization, symmetric systems 96
Realization, tridiagonal form 115
Realization, two-sided projections 353
Reconstructibility problem 76
Recursive rational interpolation 114
Recursive rational interpolation, cascade interconnection 114
Recursive rational interpolation, cascade interconnection, continued fractions 114
Recursive rational interpolation, cascade interconnection, scalar systems 114
Recursive rational interpolation, cascade interconnection, tridiagonal realization 115
Riccati equations 161 207 217 228 229 231—233
Riccati equations, bounded real case 231
Riccati equations, dissipative systems 161
Riccati equations, positive real case 232
Row reduced matrices 112
Row reduced matrices, row degrees 112
Schmidt — Eckart — Young — Mirsky theorem 37
Schur decomposition 28 320 323
Semidiscrete decomposition 41
Shift operator 59
Shift, rational interpolation 107
Sign function and Lyapunov equations 184
Silverman realization algorithm 92
Single-input, single-output (SISO) 60
Singular value decomposition (SVD) 5 31
Singular value decomposition (SVD), 2-norm and SVD 32
Singular value decomposition (SVD), least squares 40
Singular value decomposition (SVD), Moore — Penrose pseudoinverse 40
Singular value decomposition (SVD), optimal approximation 37
Singular value decomposition (SVD), optimal approximation, uniqueness of minimizer 38
Singular value decomposition (SVD), properties of 35
Singular value decomposition (SVD), Schmidt — Eckart — Young — Mirsky theorem 37
Singular value decomposition (SVD), semidiscrete decomposition 41
Singular value decomposition (SVD), short form of 35
Singular value decomposition (SVD), singular value and eigenvalue decompositions 36
Singular value decomposition (SVD), singular value and eigenvalue decompositions, pseudospectra 37
Singular value decomposition (SVD), singular values 31
Singular value decomposition (SVD), singular vectors 31
Singular value decomposition (SVD), symmetric matrices 37
Singular values, convolution operator, continuous time 130
Singular values, convolution operator, discrete-time 128
Singular values, Hankel operator 138
Singular values, Hankel operator, continuous-time 139
Singular values, Hankel operator, cross gramian 140
Singular values, Hankel operator, discrete-time 138
Singular values, Hankel operator, lemma 139
Software for model reduction 415
Spectrum, convolution operator 128
Stability 150
Stability of algorithms 44
Stability,  stability 152
Stability, asymptotic stability 151
Stability, BIBO stability 151
Stability, external stability 152
Stability, internal stability 152
Stability, Lyapunov equation 153
Stability, Lyapunov function 152
Stability, Lyapunov stability 152
Stabilizability 73
State 59
State, construction 89
State, equations 63
State, observation 74
State, transformation 66
Stein (discrete-Lyapunov) equation 79
Sylvester and Lyapunov equations 173
Sylvester and Lyapunov equations in Schur basis 191
| Sylvester and Lyapunov equations, algorithms 200
Sylvester and Lyapunov equations, Bartels — Stewart algorithm 191
Sylvester and Lyapunov equations, characteristic polynomial methods 179
Sylvester and Lyapunov equations, complex integration method 176
Sylvester and Lyapunov equations, eigenvalue/eigenvector method 178
Sylvester and Lyapunov equations, generalized reachability/observability matrices 179
Sylvester and Lyapunov equations, invariant subspace method 184
Sylvester and Lyapunov equations, Kronecker product method 175
Sylvester and Lyapunov equations, numerical issues, condition number of solutions 203
Sylvester and Lyapunov equations, numerical issues, forward/backward stability 201
Sylvester and Lyapunov equations, sign function method 184
Sylvester and Lyapunov equations, triangular coefficients 191
Sylvester equations, approximate balancing 375
Sylvester equations, connection with projectors 356
Sylvester equations, Krylov, connection with 366
Symbol, transfer function 128
Symmetric realizations 96
Systems, unstable 154
Systems, all-pass (unitary) 156
Systems, approximation, air quality simulations 16
Systems, approximation, cooling of steel 24
Systems, approximation, elk sensor 22
Systems, approximation, honeycomb vibrations 17
Systems, approximation, international space station 20
Systems, approximation, linear systems 8
Systems, approximation, methods 10
Systems, approximation, micromirrors 22
Systems, approximation, molecular dynamics 18
Systems, approximation, motivating examples 11
Systems, approximation, passive devices 11
Systems, approximation, problem definition 7
Systems, approximation, projection, by 8
Systems, approximation, properties 7
Systems, approximation, vibration/acoustic systems 20
Systems, approximation, vibration/CVD reactors 21
Systems, approximation, weather prediction 13
Systems, balanced representation 207
Systems, balanced representation, balanced truncation 211
Systems, balanced representation, bounded real balancing 231
Systems, balanced representation, canonical form 224
Systems, balanced representation, definition 210
Systems, balanced representation, frequency weighted balancing 235 237
Systems, balanced representation, frequency weighted balancing (gramians) 236 239
Systems, balanced representation, Lyapunov balancing 229
Systems, balanced representation, positive real balancing 232
Systems, balanced representation, positive real balancing, error bound 234
Systems, balanced representation, simultaneous diagonalization 210
Systems, balanced representation, stochastic balancing 229
Systems, balanced representation, stochastic balancing, multiplicative error bound 230
Systems, balanced representation, time-limited balancing 241
Systems, balanced representation, types of balancing 228
Systems, balanced representation, unstable systems 242
Systems, balanced representation, variational interpretation 211
Systems, behavioral framework 62
Systems, bilinear transformation discrete, continuous 87
Systems, causal 60 61
Systems, classical framework 62
Systems, complexity 7
Systems, construction of state 89
Systems, continuous-time 7 61
Systems, contractive 169
Systems, control 3
Systems, controllability 73
Systems, convolution operator 61
Systems, definition 6
Systems, detectability 77
Systems, dimension 64
Systems, discrete-time 7 60
Systems, dissipative 159
Systems, dissipative, available storage 159
Systems, dissipative, bounded real lemma 169
Systems, dissipative, dissipation inequality 159
Systems, dissipative, linear system, quadratic supply 160
Systems, dissipative, LMI 161
Systems, dissipative, network synthesis 169
Systems, dissipative, positive real lemma 163
Systems, dissipative, required supply 159
Systems, dissipative, Riccati equation 161
Systems, dissipative, storage function 159
Systems, dissipative, supply function 159
Systems, duality 76
Systems, dynamics 63
Systems, equivalent system triples 66
Systems, external description 60
Systems, external description, definition 62
Systems, Hankel matrix 90
Systems, implicit 7
Systems, impulse response 60 62 65
Systems, inputs and outputs 7
Systems, internal description 63 64
Systems, linear versus nonlinear 5
Systems, Markov parameters 62
Systems, McMillan degree 96 100
Systems, MIMO 60
Systems, minimal realization 93
Systems, observability 75
Systems, output equations 63
Systems, passive 163
Systems, reachability 67
Systems, reachability matrix 67
Systems, reachability, distance to 74
Systems, reachable canonical decomposition 71
Systems, realization 88
Systems, reconstructibility 76
Systems, simulation 3
Systems, SISO 60
Systems, stability 150
Systems, stability, stability 152
Systems, stability, asymptotic stability 151
Systems, stability, BIBO stability 151
Systems, stability, external stability 152
Systems, stability, internal stability 152
Systems, stability, Lyapunov equation 153
Systems, stability, Lyapunov function 152
Systems, stability, Lyapunov stability 152
Systems, stabilizability 73
Systems, stable 64
Systems, state 7
Systems, state equations 63
Systems, state transformation 66
Systems, time invariant 61
Systems, time-invariant 60
Systems, transfer function 62 65
Systems, unstable -norm of 154
Toeplitz matrix 60
Toeplitz matrix, circulant 129
Toeplitz operator 128
Transfer function 62 65
Transfer function, symbol 128
Transformation, bilinear discrete, continuous systems 87
Trapezoidal rule and Smith methods 387
Unitary dilation in Hankel-norm approximation 256
Unitary dilation in Hankel-norm approximation, optimal case 258
Unitary dilation in Hankel-norm approximation, suboptimal case 258
Weighting pattern 59
Weighting pattern, kernel 61
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