-
1
-
-
0037103431
-
On the decay rate of Hankel singular values and related issues
-
Antoulas, A., Sorensen, D., Zhou, Y.: On the decay rate of Hankel singular values and related issues. Syst. Control Lett. 46(5), 323-342 (2002).
-
(2002)
Syst. Control Lett.
, vol.46
, Issue.5
, pp. 323-342
-
-
Antoulas, A.1
Sorensen, D.2
Zhou, Y.3
-
2
-
-
84856024767
-
An error analysis for rational Galerkin projection applied to the Sylvester equation
-
Beckermann, B.: An error analysis for rational Galerkin projection applied to the Sylvester equation. SIAM J. Numer. Anal. 49, 2430 (2011).
-
(2011)
SIAM J. Numer. Anal.
, vol.49
, pp. 2430
-
-
Beckermann, B.1
-
3
-
-
84878964448
-
2-model reduction of linear parameter-varying systems
-
doi: 10. 1002/pamm. 201110391
-
2-model reduction of linear parameter-varying systems. Proc. Appl. Math. Mech. 11(1), 805-806 (2011). doi: 10. 1002/pamm. 201110391.
-
(2011)
Proc. Appl. Math. Mech
, vol.11
, Issue.1
, pp. 805-806
-
-
Benner, P.1
Breiten, T.2
-
5
-
-
84867292802
-
2-model reduction of bilinear control systems
-
2-model reduction of bilinear control systems. SIAM J. Matrix Anal. Appl. 33(3), 859-885 (2012).
-
(2012)
SIAM J. Matrix Anal. Appl
, vol.33
, Issue.3
, pp. 859-885
-
-
Benner, P.1
Breiten, T.2
-
6
-
-
79957460056
-
Lyapunov equations, energy functionals, and model order reduction of bilinear and stochastic systems
-
Benner, P., Damm, T.: Lyapunov equations, energy functionals, and model order reduction of bilinear and stochastic systems. SIAM J. Control Optim. 49(2), 686-711 (2011).
-
(2011)
SIAM J. Control Optim.
, vol.49
, Issue.2
, pp. 686-711
-
-
Benner, P.1
Damm, T.2
-
7
-
-
55749097248
-
Numerical solution of large Lyapunov equations, Riccati equations, and linear-quadratic control problems
-
Benner, P., Li, J. R., Penzl, T.: Numerical solution of large Lyapunov equations, Riccati equations, and linear-quadratic control problems. Numer. Linear Algebra Appl. 15(9), 755-777 (2008).
-
(2008)
Numer. Linear Algebra Appl.
, vol.15
, Issue.9
, pp. 755-777
-
-
Benner, P.1
Li, J.R.2
Penzl, T.3
-
8
-
-
70349739586
-
On the ADI method for Sylvester equations
-
Benner, P., Li, R., Truhar, N.: On the ADI method for Sylvester equations. J. Comput. Appl. Math. 233(4), 1035-1045 (2009).
-
(2009)
J. Comput. Appl. Math.
, vol.233
, Issue.4
, pp. 1035-1045
-
-
Benner, P.1
Li, R.2
Truhar, N.3
-
9
-
-
78649284625
-
Linear-quadratic regulator design for optimal cooling of steel profiles
-
SFB393/05-05, Sonderforschungsbereich 393 Parallele Numerische Simulation für Physik und Kontinuumsmechanik, TU Chemnitz, 09107 Chemnitz, FRG,Available from
-
Benner, P., Saak, J.: Linear-quadratic regulator design for optimal cooling of steel profiles. Tech. Rep. SFB393/05-05, Sonderforschungsbereich 393 Parallele Numerische Simulation für Physik und Kontinuumsmechanik, TU Chemnitz, 09107 Chemnitz, FRG (2005). Available from http://www. tu-chemnitz. de/sfb393.
-
(2005)
Tech. Rep
-
-
Benner, P.1
Saak, J.2
-
10
-
-
34147210549
-
Krylov subspaces from bilinear representations of nonlinear systems
-
Condon, M., Ivanov, R.: Krylov subspaces from bilinear representations of nonlinear systems. COMPEL 26, 11-26 (2007).
-
(2007)
Compel
, vol.26
, pp. 11-26
-
-
Condon, M.1
Ivanov, R.2
-
11
-
-
0000832841
-
Realization and structure theory of bilinear dynamical systems
-
D'Alessandro, P., Isidori, A., Ruberti, A.: Realization and structure theory of bilinear dynamical systems. SIAM J. Control Optim. 12(3), 517-535 (1974).
-
(1974)
SIAM J. Control Optim
, vol.12
, Issue.3
, pp. 517-535
-
-
D'Alessandro, P.1
Isidori, A.2
Ruberti, A.3
-
13
-
-
55749085866
-
Direct methods and ADI-preconditioned Krylov subspace methods for generalized Lyapunov equations
-
Damm, T.: Direct methods and ADI-preconditioned Krylov subspace methods for generalized Lyapunov equations. Numer. Linear Algebra Appl. 15(9), 853-871 (2008).
-
(2008)
Numer. Linear Algebra Appl
, vol.15
, Issue.9
, pp. 853-871
-
-
Damm, T.1
-
14
-
-
0024718109
-
Canonical forms for bilinear systems
-
Dorissen, H.: Canonical forms for bilinear systems. Syst. Control Lett. 13(2), 153-160 (1989).
-
(1989)
Syst. Control Lett.
, vol.13
, Issue.2
, pp. 153-160
-
-
Dorissen, H.1
-
15
-
-
81555222620
-
Analysis of the rational Krylov subspace and ADI methods for solving the Lyapunov equation
-
Druskin, V., Knizhnerman, L., Simoncini, V.: Analysis of the rational Krylov subspace and ADI methods for solving the Lyapunov equation. SIAM J. Numer. Anal. 49, 1875-1898 (2011).
-
(2011)
SIAM J. Numer. Anal.
, vol.49
, pp. 1875-1898
-
-
Druskin, V.1
Knizhnerman, L.2
Simoncini, V.3
-
16
-
-
79959705270
-
Adaptive rational Krylov subspaces for large-scale dynamical systems
-
Druskin, V., Simoncini, V.: Adaptive rational Krylov subspaces for large-scale dynamical systems. Syst. Control Lett. 60, 546-560 (2011).
-
(2011)
Syst. Control Lett.
, vol.60
, pp. 546-560
-
-
Druskin, V.1
Simoncini, V.2
-
17
-
-
84878991182
-
An alternative way of solving large Lyapunov equations
-
doi: 10. 1002/pamm. 201010266
-
Eppler, A. K., Bollhöfer, M.: An alternative way of solving large Lyapunov equations. Proc. Appl. Math. Mech. 10(1), 547-548. doi: 10. 1002/pamm. 201010266.
-
Proc. Appl. Math. Mech
, vol.10
, Issue.1
, pp. 547-548
-
-
Eppler, A.K.1
Bollhöfer, M.2
-
18
-
-
84900557277
-
A structure preserving FGMRES method for solving large Lyapunov equations
-
In: Günther, M., Bartel, A., Brunk, M., Schöps, S., Striebel, M. (eds.),Springer, Berlin, doi: 10. 1007/978-3-642-25100-9-15
-
Eppler, A., Bollhöfer, M.: A structure preserving FGMRES method for solving large Lyapunov equations. In: Günther, M., Bartel, A., Brunk, M., Schöps, S., Striebel, M. (eds.) Progress in Industrial Mathematics at ECMI 2010, Mathematics in Industry, vol. 17, pp. 131-136. Springer, Berlin (2012). doi: 10. 1007/978-3-642-25100-9-15.
-
(2012)
Progress in Industrial Mathematics at ECMI 2010, Mathematics in Industry
, vol.17
, pp. 131-136
-
-
Eppler, A.1
Bollhöfer, M.2
-
19
-
-
84870053382
-
On the ADI method for the Sylvester equation and the optimal-H2 points
-
doi: 10. 1016/j. apnum. 2012. 10. 001
-
Flagg, G. M., Gugercin, S.: On the ADI method for the Sylvester equation and the optimal-H2 points. Appl. Numer. Math. 64, 50-58 (2013). doi: 10. 1016/j. apnum. 2012. 10. 001.
-
(2013)
Appl. Numer. Math
, vol.64
, pp. 50-58
-
-
Flagg, G.M.1
Gugercin, S.2
-
20
-
-
3042756404
-
Existence and computation of low Kronecker-rank approximations for large linear systems of tensor product structure
-
Grasedyck, L.: Existence and computation of low Kronecker-rank approximations for large linear systems of tensor product structure. Computing 72(3-4), 247-265 (2004).
-
(2004)
Computing
, vol.72
, Issue.3-4
, pp. 247-265
-
-
Grasedyck, L.1
-
21
-
-
10044281868
-
Existence of a low rank or H-matrix approximant to the solution of a sylvester equation
-
doi: 10. 1002/nla. 366
-
Grasedyck, L.: Existence of a low rank or H-matrix approximant to the solution of a sylvester equation. Numer. Linear Algebra Appl. 11(4), 371-389 (2004). doi: 10. 1002/nla. 366.
-
(2004)
Numer. Linear Algebra Appl
, vol.11
, Issue.4
, pp. 371-389
-
-
Grasedyck, L.1
-
25
-
-
0004151494
-
-
Cambridge: Cambridge University Press
-
Horn, R., Johnson, C.: Matrix Analysis. Cambridge University Press, Cambridge (1990).
-
(1990)
Matrix Analysis
-
-
Horn, R.1
Johnson, C.2
-
26
-
-
0028377922
-
Krylov subspace methods for solving large Lyapunov equations
-
Jaimoukha, I., Kasenally, E.: Krylov subspace methods for solving large Lyapunov equations. SIAM J. Numer. Anal. 31, 227-251 (1994).
-
(1994)
SIAM J. Numer. Anal.
, vol.31
, pp. 227-251
-
-
Jaimoukha, I.1
Kasenally, E.2
-
27
-
-
33745469648
-
Projection methods for large Lyapunov matrix equations
-
Jbilou, K., Riquet, A. J.: Projection methods for large Lyapunov matrix equations. Linear Algebra Appl. 415(2-3), 344-358 (2006).
-
(2006)
Linear Algebra Appl.
, vol.415
, Issue.2-3
, pp. 344-358
-
-
Jbilou, K.1
Riquet, A.J.2
-
28
-
-
68649096448
-
Tensor decompositions and applications
-
doi:10.1137/07070111X
-
Kolda, T., Bader, B.: Tensor decompositions and applications. SIAM Rev. 51(3), 455-500 (2009). doi: 10. 1137/07070111X.
-
(2009)
SIAM Rev.
, vol.51
, Issue.3
, pp. 455-500
-
-
Kolda, T.1
Bader, B.2
-
29
-
-
77956045829
-
Krylov subspace methods for linear systems with tensor product structure
-
Kressner, D., Tobler, C.: Krylov subspace methods for linear systems with tensor product structure. SIAM J. Matrix Anal. Appl. 31(4), 1688-1714 (2010).
-
(2010)
SIAM J. Matrix Anal. Appl.
, vol.31
, Issue.4
, pp. 1688-1714
-
-
Kressner, D.1
Tobler, C.2
-
30
-
-
84856290662
-
Low-rank tensor Krylov subspace methods for parametrized linear systems
-
Kressner, D., Tobler, C.: Low-rank tensor Krylov subspace methods for parametrized linear systems. SIAM J. Matrix Anal. Appl. 32(4), 1288-1316 (2011).
-
(2011)
SIAM J. Matrix Anal. Appl.
, vol.32
, Issue.4
, pp. 1288-1316
-
-
Kressner, D.1
Tobler, C.2
-
31
-
-
80053926097
-
Preconditioned low-rank methods for high-dimensional elliptic PDE eigenvalue problems
-
Kressner, D., Tobler, C.: Preconditioned low-rank methods for high-dimensional elliptic PDE eigenvalue problems. CMAM 11(3), 363-381 (2011).
-
(2011)
Cmam
, vol.11
, Issue.3
, pp. 363-381
-
-
Kressner, D.1
Tobler, C.2
-
32
-
-
0037287244
-
Low rank solution of Lyapunov equations
-
Li, J. R., White, J.: Low rank solution of Lyapunov equations. SIAM J. Matrix Anal. Appl. 24(1), 260-280 (2002).
-
(2002)
SIAM J. Matrix Anal. Appl.
, vol.24
, Issue.1
, pp. 260-280
-
-
Li, J.R.1
White, J.2
-
33
-
-
0001082478
-
Eigenvalue decay bounds for solutions of Lyapunov equations: the symmetric case
-
Penzl, T.: Eigenvalue decay bounds for solutions of Lyapunov equations: the symmetric case. Syst. Control Lett. 40(2), 139-144 (2000).
-
(2000)
Syst. Control Lett.
, vol.40
, Issue.2
, pp. 139-144
-
-
Penzl, T.1
-
34
-
-
0003553624
-
-
Baltimore: The Johns Hopkins University Press
-
Rugh, W.: Nonlinear System Theory. The Johns Hopkins University Press, Baltimore (1982).
-
(1982)
Nonlinear System Theory
-
-
Rugh, W.1
-
35
-
-
0000175612
-
Numerical solution of large Lyapunov equation
-
M. A. Kaashoek, J. H. Schuppenvan, and A. C. M. Ran (Eds.), Basel: Birkhauser
-
Saad, Y.: Numerical solution of large Lyapunov equation. In: Kaashoek, M. A., van Schuppen, J. H., Ran, A. C. M. (eds.) Signal Processing, Scattering, Operator Theory and Numerical Methods, pp. 503-511. Birkhauser, Basel (1990).
-
(1990)
Signal Processing, Scattering, Operator Theory and Numerical Methods
, pp. 503-511
-
-
Saad, Y.1
-
36
-
-
44649084929
-
A new iterative method for solving large-scale Lyapunov matrix equations
-
Simoncini, V.: A new iterative method for solving large-scale Lyapunov matrix equations. SIAM J. Sci. Comput. 29(3), 1268-1288 (2007).
-
(2007)
SIAM J. Sci. Comput.
, vol.29
, Issue.3
, pp. 1268-1288
-
-
Simoncini, V.1
-
37
-
-
10044265621
-
Bounds on eigenvalue decay rates and sensitivity of solutions to Lyapunov equations
-
Rice University, Houston, TX,Available online from
-
Sorensen, D., Zhou, Y.: Bounds on eigenvalue decay rates and sensitivity of solutions to Lyapunov equations. Tech. Rep. TR02-07, Dept. of Comp. Appl. Math., Rice University, Houston, TX (2002). Available online from http://www. caam. rice. edu/caam/trs/tr02. html#TR02.
-
(2002)
Tech. Rep. TR02-07, Dept. of Comp. Appl. Math
-
-
Sorensen, D.1
Zhou, Y.2
-
38
-
-
0003252589
-
Numerical methods based on Sinc and analytic functions
-
Springer, New York
-
Stenger, F.: Numerical methods based on Sinc and analytic functions. In: Springer Series in Computational Mathematics, vol. 20. Springer, New York (1993).
-
(1993)
Springer Series in Computational Mathematics
, vol.20
-
-
Stenger, F.1
-
39
-
-
38249030580
-
Iterative solution of the Lyapunov matrix equation
-
Wachspress, E.: Iterative solution of the Lyapunov matrix equation. Appl. Math. Lett. 107, 87-90 (1988).
-
(1988)
Appl. Math. Lett.
, vol.107
, pp. 87-90
-
-
Wachspress, E.1
|