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Deflation by restriction for the inverse-free preconditioned Krylov subspace method
Projection-based model reduction for time-varying descriptor systems: New results
1. | Department of Mathematics and Physics, North South University, Dhaka, Bangladesh |
References:
[1] |
Z. Bai, Krylov subspace techniques for reduced-order modeling for large-scale dynamical system, App. Numer. Math, 43(1-2) (2002), 9-44.
doi: 10.1016/S0168-9274(02)00116-2. |
[2] |
P. Benner, Solving large-scale control problems, IEEE Control System Magazine, 24 (2004), 44-59. |
[3] |
P. Benner, Numerical linear algebra for model reduction in control and simulation, GAMM Mitteilungen, 23 (2006), 275-296.
doi: 10.1002/gamm.201490034. |
[4] |
S. Bittanti and P. Colaneri, Periodic Systems: Filtering and Control, 1st edition, Springer-Verlag, London, 2009. |
[5] |
H. G. Brachtendorf, Theorie und Analyse von Autonomen und Quasiperiodisch Angeregten Elektrischen Netzwerken. Eine Algorithmisch Orientierte Betrachtung, Habilitation thesis, University of Bremen, Germany, 2001. |
[6] |
R. L. Burden and J. D. Faires, Numerical Analysis, Ninth edition, Brooks/Cole, Boston, USA, 2011. |
[7] |
I. Elfadel and D. D. Ling, A block Arnoldi algorithm for multipoint passive model-order reduction of multiport RLC networks, in IEEE/ACM International Conference on Computer-Aided Design, IEEE, (1997), 66-71. |
[8] |
R. Freund, Model reduction methods based on Krylov subspaces, Acta Numerica, 12 (2003), 267-319.
doi: 10.1017/S0962492902000120. |
[9] |
G. Golub and C. Van Loan, Matrix Computations, 3rd edition, Johns Hopkins University Press, Baltimore, 1996. |
[10] |
E. J. Grimme, Kryloy projection methods for model reduction, Ph.D. thesis, University of Illinois at Urbana, Champaign, 1997. |
[11] |
S. Gugercin, An iterative SVD-KRYLOV based method for model reduction of large-scale dynamical systems, in 44'th IEEE Conference on Decision and Control and the European control conference, IEEE, 2005, 5905-5910. |
[12] |
S. Gugercin, A. C. Antoulas and C. Beattie, H2 model reduction for large-scale linear dynamical systems, SIAM J. Matrix Anal. Appl, 30 (2008), 609-638.
doi: 10.1137/060666123. |
[13] |
M.-S. Hossain and P. Benner, Projection-based model reduction for time-varying descriptor systems using recycled Krylov subspaces, in Appllied Mathematics and Mechanics, WILEY-VCH Verlag, 2008, 10081-10084. |
[14] |
M. Nakhla and E. Gad, Efficient model reduction of linear time-varying systems via compressed transient system function, in Conference on Design, automation and test in Europe, IEEE, 2002, 916-922. |
[15] |
M. Nakhla and E. Gad, Efficient model reduction of linear periodically time-varying systems via compressed transient system function, IEEE Transactions on Circuit and Systems, 52 (2005), 1188-1204.
doi: 10.1109/TCSI.2005.846661. |
[16] |
T. Penzl, Algorithms for model reduction of large dynamical systems, Linear Algebra Appl., 415 (2006), 322-343.
doi: 10.1016/j.laa.2006.01.007. |
[17] |
J. Phillips, Model reduction of time-varying linear systems using multipoint Krylov-subspace projectors, in International Conference on Computer-Aided Design, ACM, 1998, 96-102. |
[18] |
J. Phillips, Projection-based approaches for model reduction of weakly nonlinear time-varying systems, IEEE Trans. Computer-Aided Design, 22 (2003), 171-187. |
[19] |
A. Rahman and M. S. Hossain, Svd-Krylov based model reduction for time-varying periodic descriptor systems, in 2nd International Conference on Electrical Engineering and Information Technology, IEEE, 2015. |
[20] |
J. Roychowdhury, Reduced-order modeling of time-varying systems, IEEE Control Systems Magazine, 46 (1999), 1273-1288. |
[21] |
J. Roychowdhury, Reduced-order modelling of linear time-varying systems, in ASP-DAC '99. Asia and South Pacific, IEEE, 1999, 53-56. |
[22] |
Y. Saad, Overview of Krylov subspace methods with applications to control problems, in International Symposium MTNS-89 on Signal Processing, Scattering and Operator Theory, and Numerical Methods, Birkhauser Verlag AG, 1990. |
[23] |
Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd edition, SIAM, Philadelphia, 2003.
doi: 10.1137/1.9780898718003. |
[24] |
B. Salimbahrami, B. Lohmann, T. Bechtold and J. Korvink, Two-sided Arnoldi algorithm and its application in order reduction of MEMS, in 4th Fourth International Conference on Mathematical Modelling (eds. I. Troch and F. Breitenecker), Vienna, 2003, 1021-1028. |
[25] |
S. B. Salimbahrami, Structure Preserving Order Reduction of Large Scale Second Order Models, Ph.D. thesis, Technische Universität München, Fakultät für Maschinenwesen, Germany, 2005. |
[26] |
R. E. Skelton, M. Oliveira and J. Han, System modeling and model reduction,, Paper available from: , ().
|
[27] |
T. Stykel, Low-rank iterative methods for projected generalized Lyapunov equations, Electron. Trans. Numer. Anal., 30 (2008), 187-202. |
[28] |
R. Telichevesky, J. White and K. Kundert, Efficient steady-state analysis based on matrix-free Krylov-subspace methods, in 32rd Design Automation Conference, IEEE, 1995, 480-484. |
[29] |
R. Telichevesky, J. White and K. Kundert, Efficient AC and noise analysis of two-tone RF circuits, in 33rd annual Design Automation Conference, IEEE, 1996, 292-297. |
[30] |
A. A. Vaidyanathan, Multirate digital filters, filters banks, polyphase networks, and applications: A tutorial, in IEEE Proceedings, IEEE, 1990, 56-93. |
[31] | |
[32] |
B. Yang and D. Feng, Efficient finite-difference method for quasi-periodic steady-state and small signal analyses, in IEEE/ACM International Conference on Computer-Aided Design, IEEE, 2000, 272-276. |
[33] |
L. Zadeh, Frequency analysis of variable networks, IEEE Transactions on Circuits and Systems, 38 (1950), 291-299. |
show all references
References:
[1] |
Z. Bai, Krylov subspace techniques for reduced-order modeling for large-scale dynamical system, App. Numer. Math, 43(1-2) (2002), 9-44.
doi: 10.1016/S0168-9274(02)00116-2. |
[2] |
P. Benner, Solving large-scale control problems, IEEE Control System Magazine, 24 (2004), 44-59. |
[3] |
P. Benner, Numerical linear algebra for model reduction in control and simulation, GAMM Mitteilungen, 23 (2006), 275-296.
doi: 10.1002/gamm.201490034. |
[4] |
S. Bittanti and P. Colaneri, Periodic Systems: Filtering and Control, 1st edition, Springer-Verlag, London, 2009. |
[5] |
H. G. Brachtendorf, Theorie und Analyse von Autonomen und Quasiperiodisch Angeregten Elektrischen Netzwerken. Eine Algorithmisch Orientierte Betrachtung, Habilitation thesis, University of Bremen, Germany, 2001. |
[6] |
R. L. Burden and J. D. Faires, Numerical Analysis, Ninth edition, Brooks/Cole, Boston, USA, 2011. |
[7] |
I. Elfadel and D. D. Ling, A block Arnoldi algorithm for multipoint passive model-order reduction of multiport RLC networks, in IEEE/ACM International Conference on Computer-Aided Design, IEEE, (1997), 66-71. |
[8] |
R. Freund, Model reduction methods based on Krylov subspaces, Acta Numerica, 12 (2003), 267-319.
doi: 10.1017/S0962492902000120. |
[9] |
G. Golub and C. Van Loan, Matrix Computations, 3rd edition, Johns Hopkins University Press, Baltimore, 1996. |
[10] |
E. J. Grimme, Kryloy projection methods for model reduction, Ph.D. thesis, University of Illinois at Urbana, Champaign, 1997. |
[11] |
S. Gugercin, An iterative SVD-KRYLOV based method for model reduction of large-scale dynamical systems, in 44'th IEEE Conference on Decision and Control and the European control conference, IEEE, 2005, 5905-5910. |
[12] |
S. Gugercin, A. C. Antoulas and C. Beattie, H2 model reduction for large-scale linear dynamical systems, SIAM J. Matrix Anal. Appl, 30 (2008), 609-638.
doi: 10.1137/060666123. |
[13] |
M.-S. Hossain and P. Benner, Projection-based model reduction for time-varying descriptor systems using recycled Krylov subspaces, in Appllied Mathematics and Mechanics, WILEY-VCH Verlag, 2008, 10081-10084. |
[14] |
M. Nakhla and E. Gad, Efficient model reduction of linear time-varying systems via compressed transient system function, in Conference on Design, automation and test in Europe, IEEE, 2002, 916-922. |
[15] |
M. Nakhla and E. Gad, Efficient model reduction of linear periodically time-varying systems via compressed transient system function, IEEE Transactions on Circuit and Systems, 52 (2005), 1188-1204.
doi: 10.1109/TCSI.2005.846661. |
[16] |
T. Penzl, Algorithms for model reduction of large dynamical systems, Linear Algebra Appl., 415 (2006), 322-343.
doi: 10.1016/j.laa.2006.01.007. |
[17] |
J. Phillips, Model reduction of time-varying linear systems using multipoint Krylov-subspace projectors, in International Conference on Computer-Aided Design, ACM, 1998, 96-102. |
[18] |
J. Phillips, Projection-based approaches for model reduction of weakly nonlinear time-varying systems, IEEE Trans. Computer-Aided Design, 22 (2003), 171-187. |
[19] |
A. Rahman and M. S. Hossain, Svd-Krylov based model reduction for time-varying periodic descriptor systems, in 2nd International Conference on Electrical Engineering and Information Technology, IEEE, 2015. |
[20] |
J. Roychowdhury, Reduced-order modeling of time-varying systems, IEEE Control Systems Magazine, 46 (1999), 1273-1288. |
[21] |
J. Roychowdhury, Reduced-order modelling of linear time-varying systems, in ASP-DAC '99. Asia and South Pacific, IEEE, 1999, 53-56. |
[22] |
Y. Saad, Overview of Krylov subspace methods with applications to control problems, in International Symposium MTNS-89 on Signal Processing, Scattering and Operator Theory, and Numerical Methods, Birkhauser Verlag AG, 1990. |
[23] |
Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd edition, SIAM, Philadelphia, 2003.
doi: 10.1137/1.9780898718003. |
[24] |
B. Salimbahrami, B. Lohmann, T. Bechtold and J. Korvink, Two-sided Arnoldi algorithm and its application in order reduction of MEMS, in 4th Fourth International Conference on Mathematical Modelling (eds. I. Troch and F. Breitenecker), Vienna, 2003, 1021-1028. |
[25] |
S. B. Salimbahrami, Structure Preserving Order Reduction of Large Scale Second Order Models, Ph.D. thesis, Technische Universität München, Fakultät für Maschinenwesen, Germany, 2005. |
[26] |
R. E. Skelton, M. Oliveira and J. Han, System modeling and model reduction,, Paper available from: , ().
|
[27] |
T. Stykel, Low-rank iterative methods for projected generalized Lyapunov equations, Electron. Trans. Numer. Anal., 30 (2008), 187-202. |
[28] |
R. Telichevesky, J. White and K. Kundert, Efficient steady-state analysis based on matrix-free Krylov-subspace methods, in 32rd Design Automation Conference, IEEE, 1995, 480-484. |
[29] |
R. Telichevesky, J. White and K. Kundert, Efficient AC and noise analysis of two-tone RF circuits, in 33rd annual Design Automation Conference, IEEE, 1996, 292-297. |
[30] |
A. A. Vaidyanathan, Multirate digital filters, filters banks, polyphase networks, and applications: A tutorial, in IEEE Proceedings, IEEE, 1990, 56-93. |
[31] | |
[32] |
B. Yang and D. Feng, Efficient finite-difference method for quasi-periodic steady-state and small signal analyses, in IEEE/ACM International Conference on Computer-Aided Design, IEEE, 2000, 272-276. |
[33] |
L. Zadeh, Frequency analysis of variable networks, IEEE Transactions on Circuits and Systems, 38 (1950), 291-299. |
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