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Deflation by restriction for the inversefree preconditioned Krylov subspace method
Projectionbased model reduction for timevarying descriptor systems: New results
1.  Department of Mathematics and Physics, North South University, Dhaka, Bangladesh 
References:
[1] 
Z. Bai, Krylov subspace techniques for reducedorder modeling for largescale dynamical system, App. Numer. Math, 43(12) (2002), 944. doi: 10.1016/S01689274(02)001162. Google Scholar 
[2] 
P. Benner, Solving largescale control problems, IEEE Control System Magazine, 24 (2004), 4459. Google Scholar 
[3] 
P. Benner, Numerical linear algebra for model reduction in control and simulation, GAMM Mitteilungen, 23 (2006), 275296. doi: 10.1002/gamm.201490034. Google Scholar 
[4] 
S. Bittanti and P. Colaneri, Periodic Systems: Filtering and Control, 1st edition, SpringerVerlag, London, 2009. Google Scholar 
[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. Google Scholar 
[6] 
R. L. Burden and J. D. Faires, Numerical Analysis, Ninth edition, Brooks/Cole, Boston, USA, 2011. Google Scholar 
[7] 
I. Elfadel and D. D. Ling, A block Arnoldi algorithm for multipoint passive modelorder reduction of multiport RLC networks, in IEEE/ACM International Conference on ComputerAided Design, IEEE, (1997), 6671. Google Scholar 
[8] 
R. Freund, Model reduction methods based on Krylov subspaces, Acta Numerica, 12 (2003), 267319. doi: 10.1017/S0962492902000120. Google Scholar 
[9] 
G. Golub and C. Van Loan, Matrix Computations, 3rd edition, Johns Hopkins University Press, Baltimore, 1996. Google Scholar 
[10] 
E. J. Grimme, Kryloy projection methods for model reduction, Ph.D. thesis, University of Illinois at Urbana, Champaign, 1997. Google Scholar 
[11] 
S. Gugercin, An iterative SVDKRYLOV based method for model reduction of largescale dynamical systems, in 44'th IEEE Conference on Decision and Control and the European control conference, IEEE, 2005, 59055910. Google Scholar 
[12] 
S. Gugercin, A. C. Antoulas and C. Beattie, H_{2} model reduction for largescale linear dynamical systems, SIAM J. Matrix Anal. Appl, 30 (2008), 609638. doi: 10.1137/060666123. Google Scholar 
[13] 
M.S. Hossain and P. Benner, Projectionbased model reduction for timevarying descriptor systems using recycled Krylov subspaces, in Appllied Mathematics and Mechanics, WILEYVCH Verlag, 2008, 1008110084. Google Scholar 
[14] 
M. Nakhla and E. Gad, Efficient model reduction of linear timevarying systems via compressed transient system function, in Conference on Design, automation and test in Europe, IEEE, 2002, 916922. Google Scholar 
[15] 
M. Nakhla and E. Gad, Efficient model reduction of linear periodically timevarying systems via compressed transient system function, IEEE Transactions on Circuit and Systems, 52 (2005), 11881204. doi: 10.1109/TCSI.2005.846661. Google Scholar 
[16] 
T. Penzl, Algorithms for model reduction of large dynamical systems, Linear Algebra Appl., 415 (2006), 322343. doi: 10.1016/j.laa.2006.01.007. Google Scholar 
[17] 
J. Phillips, Model reduction of timevarying linear systems using multipoint Krylovsubspace projectors, in International Conference on ComputerAided Design, ACM, 1998, 96102. Google Scholar 
[18] 
J. Phillips, Projectionbased approaches for model reduction of weakly nonlinear timevarying systems, IEEE Trans. ComputerAided Design, 22 (2003), 171187. Google Scholar 
[19] 
A. Rahman and M. S. Hossain, SvdKrylov based model reduction for timevarying periodic descriptor systems, in 2nd International Conference on Electrical Engineering and Information Technology, IEEE, 2015. Google Scholar 
[20] 
J. Roychowdhury, Reducedorder modeling of timevarying systems, IEEE Control Systems Magazine, 46 (1999), 12731288. Google Scholar 
[21] 
J. Roychowdhury, Reducedorder modelling of linear timevarying systems, in ASPDAC '99. Asia and South Pacific, IEEE, 1999, 5356. Google Scholar 
[22] 
Y. Saad, Overview of Krylov subspace methods with applications to control problems, in International Symposium MTNS89 on Signal Processing, Scattering and Operator Theory, and Numerical Methods, Birkhauser Verlag AG, 1990. Google Scholar 
[23] 
Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd edition, SIAM, Philadelphia, 2003. doi: 10.1137/1.9780898718003. Google Scholar 
[24] 
B. Salimbahrami, B. Lohmann, T. Bechtold and J. Korvink, Twosided 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, 10211028. Google Scholar 
[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. Google Scholar 
[26] 
R. E. Skelton, M. Oliveira and J. Han, System modeling and model reduction,, Paper available from: , (). Google Scholar 
[27] 
T. Stykel, Lowrank iterative methods for projected generalized Lyapunov equations, Electron. Trans. Numer. Anal., 30 (2008), 187202. Google Scholar 
[28] 
R. Telichevesky, J. White and K. Kundert, Efficient steadystate analysis based on matrixfree Krylovsubspace methods, in 32rd Design Automation Conference, IEEE, 1995, 480484. Google Scholar 
[29] 
R. Telichevesky, J. White and K. Kundert, Efficient AC and noise analysis of twotone RF circuits, in 33rd annual Design Automation Conference, IEEE, 1996, 292297. Google Scholar 
[30] 
A. A. Vaidyanathan, Multirate digital filters, filters banks, polyphase networks, and applications: A tutorial, in IEEE Proceedings, IEEE, 1990, 5693. Google Scholar 
[31] 
E. Wachspress, The ADI Model Problem,, 1995, (). Google Scholar 
[32] 
B. Yang and D. Feng, Efficient finitedifference method for quasiperiodic steadystate and small signal analyses, in IEEE/ACM International Conference on ComputerAided Design, IEEE, 2000, 272276. Google Scholar 
[33] 
L. Zadeh, Frequency analysis of variable networks, IEEE Transactions on Circuits and Systems, 38 (1950), 291299. Google Scholar 
show all references
References:
[1] 
Z. Bai, Krylov subspace techniques for reducedorder modeling for largescale dynamical system, App. Numer. Math, 43(12) (2002), 944. doi: 10.1016/S01689274(02)001162. Google Scholar 
[2] 
P. Benner, Solving largescale control problems, IEEE Control System Magazine, 24 (2004), 4459. Google Scholar 
[3] 
P. Benner, Numerical linear algebra for model reduction in control and simulation, GAMM Mitteilungen, 23 (2006), 275296. doi: 10.1002/gamm.201490034. Google Scholar 
[4] 
S. Bittanti and P. Colaneri, Periodic Systems: Filtering and Control, 1st edition, SpringerVerlag, London, 2009. Google Scholar 
[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. Google Scholar 
[6] 
R. L. Burden and J. D. Faires, Numerical Analysis, Ninth edition, Brooks/Cole, Boston, USA, 2011. Google Scholar 
[7] 
I. Elfadel and D. D. Ling, A block Arnoldi algorithm for multipoint passive modelorder reduction of multiport RLC networks, in IEEE/ACM International Conference on ComputerAided Design, IEEE, (1997), 6671. Google Scholar 
[8] 
R. Freund, Model reduction methods based on Krylov subspaces, Acta Numerica, 12 (2003), 267319. doi: 10.1017/S0962492902000120. Google Scholar 
[9] 
G. Golub and C. Van Loan, Matrix Computations, 3rd edition, Johns Hopkins University Press, Baltimore, 1996. Google Scholar 
[10] 
E. J. Grimme, Kryloy projection methods for model reduction, Ph.D. thesis, University of Illinois at Urbana, Champaign, 1997. Google Scholar 
[11] 
S. Gugercin, An iterative SVDKRYLOV based method for model reduction of largescale dynamical systems, in 44'th IEEE Conference on Decision and Control and the European control conference, IEEE, 2005, 59055910. Google Scholar 
[12] 
S. Gugercin, A. C. Antoulas and C. Beattie, H_{2} model reduction for largescale linear dynamical systems, SIAM J. Matrix Anal. Appl, 30 (2008), 609638. doi: 10.1137/060666123. Google Scholar 
[13] 
M.S. Hossain and P. Benner, Projectionbased model reduction for timevarying descriptor systems using recycled Krylov subspaces, in Appllied Mathematics and Mechanics, WILEYVCH Verlag, 2008, 1008110084. Google Scholar 
[14] 
M. Nakhla and E. Gad, Efficient model reduction of linear timevarying systems via compressed transient system function, in Conference on Design, automation and test in Europe, IEEE, 2002, 916922. Google Scholar 
[15] 
M. Nakhla and E. Gad, Efficient model reduction of linear periodically timevarying systems via compressed transient system function, IEEE Transactions on Circuit and Systems, 52 (2005), 11881204. doi: 10.1109/TCSI.2005.846661. Google Scholar 
[16] 
T. Penzl, Algorithms for model reduction of large dynamical systems, Linear Algebra Appl., 415 (2006), 322343. doi: 10.1016/j.laa.2006.01.007. Google Scholar 
[17] 
J. Phillips, Model reduction of timevarying linear systems using multipoint Krylovsubspace projectors, in International Conference on ComputerAided Design, ACM, 1998, 96102. Google Scholar 
[18] 
J. Phillips, Projectionbased approaches for model reduction of weakly nonlinear timevarying systems, IEEE Trans. ComputerAided Design, 22 (2003), 171187. Google Scholar 
[19] 
A. Rahman and M. S. Hossain, SvdKrylov based model reduction for timevarying periodic descriptor systems, in 2nd International Conference on Electrical Engineering and Information Technology, IEEE, 2015. Google Scholar 
[20] 
J. Roychowdhury, Reducedorder modeling of timevarying systems, IEEE Control Systems Magazine, 46 (1999), 12731288. Google Scholar 
[21] 
J. Roychowdhury, Reducedorder modelling of linear timevarying systems, in ASPDAC '99. Asia and South Pacific, IEEE, 1999, 5356. Google Scholar 
[22] 
Y. Saad, Overview of Krylov subspace methods with applications to control problems, in International Symposium MTNS89 on Signal Processing, Scattering and Operator Theory, and Numerical Methods, Birkhauser Verlag AG, 1990. Google Scholar 
[23] 
Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd edition, SIAM, Philadelphia, 2003. doi: 10.1137/1.9780898718003. Google Scholar 
[24] 
B. Salimbahrami, B. Lohmann, T. Bechtold and J. Korvink, Twosided 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, 10211028. Google Scholar 
[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. Google Scholar 
[26] 
R. E. Skelton, M. Oliveira and J. Han, System modeling and model reduction,, Paper available from: , (). Google Scholar 
[27] 
T. Stykel, Lowrank iterative methods for projected generalized Lyapunov equations, Electron. Trans. Numer. Anal., 30 (2008), 187202. Google Scholar 
[28] 
R. Telichevesky, J. White and K. Kundert, Efficient steadystate analysis based on matrixfree Krylovsubspace methods, in 32rd Design Automation Conference, IEEE, 1995, 480484. Google Scholar 
[29] 
R. Telichevesky, J. White and K. Kundert, Efficient AC and noise analysis of twotone RF circuits, in 33rd annual Design Automation Conference, IEEE, 1996, 292297. Google Scholar 
[30] 
A. A. Vaidyanathan, Multirate digital filters, filters banks, polyphase networks, and applications: A tutorial, in IEEE Proceedings, IEEE, 1990, 5693. Google Scholar 
[31] 
E. Wachspress, The ADI Model Problem,, 1995, (). Google Scholar 
[32] 
B. Yang and D. Feng, Efficient finitedifference method for quasiperiodic steadystate and small signal analyses, in IEEE/ACM International Conference on ComputerAided Design, IEEE, 2000, 272276. Google Scholar 
[33] 
L. Zadeh, Frequency analysis of variable networks, IEEE Transactions on Circuits and Systems, 38 (1950), 291299. Google Scholar 
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