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Volumn 64, Issue , 2013, Pages 50-58

On the ADI method for the Sylvester equation and the optimal H-2 points

Author keywords

H2 optimal interpolation; ADI method; Rational Krylov; Sylvester equations

Indexed keywords

ADI METHOD; LOW RANK APPROXIMATIONS; LYAPUNOV EQUATION; OPTIMAL INTERPOLATION; PROJECTION METHOD; RATIONAL KRYLOV; SYLVESTER EQUATION;

EID: 84870053382     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2012.10.001     Document Type: Article
Times cited : (30)

References (43)
  • 1
    • 34047199854 scopus 로고    scopus 로고
    • Approximation of large-scale dynamical systems
    • Society for Industrial and Applied Mathematics Philadelphia, PA, USA
    • A.C. Antoulas Approximation of Large-Scale Dynamical Systems Advances in Design and Control 2005 Society for Industrial and Applied Mathematics Philadelphia, PA, USA
    • (2005) Advances in Design and Control
    • Antoulas, A.C.1
  • 3
    • 34147177796 scopus 로고    scopus 로고
    • A new projection method for solving large Sylvester equations
    • L. Bao, Y. Lin, and Y. Wei A new projection method for solving large Sylvester equations Appl. Numer. Math. 57 5-7 2007 521 532
    • (2007) Appl. Numer. Math. , vol.57 , Issue.57 , pp. 521-532
    • Bao, L.1    Lin, Y.2    Wei, Y.3
  • 4
    • 84976855597 scopus 로고
    • Algorithm 432: Solution of the matrix equation AX + XB = C
    • R.H. Bartels, and G.W. Stewart Algorithm 432: Solution of the matrix equation AX + XB = C Commun. ACM 15 9 1972 820 826
    • (1972) Commun. ACM , vol.15 , Issue.9 , pp. 820-826
    • Bartels, R.H.1    Stewart, G.W.2
  • 8
    • 55749097248 scopus 로고    scopus 로고
    • Numerical solution of large Lyapunov equations, Riccati equations, and linear-quadratic control problems
    • P. Benner, J.-R. Li, and T. Penzl Numerical solution of large Lyapunov equations, Riccati equations, and linear-quadratic control problems Numer. Linear Algebra Appl. 15 9 2008 755 777
    • (2008) Numer. Linear Algebra Appl. , vol.15 , Issue.9 , pp. 755-777
    • Benner, P.1    Li, J.-R.2    Penzl, T.3
  • 9
    • 70349739586 scopus 로고    scopus 로고
    • On the ADI method for Sylvester equations
    • P. Benner, R.-C. Li, and N. Truhar On the ADI method for Sylvester equations J. Comput. Appl. Math. 233 4 2009 1035 1045
    • (2009) J. Comput. Appl. Math. , vol.233 , Issue.4 , pp. 1035-1045
    • Benner, P.1    Li, R.-C.2    Truhar, N.3
  • 10
    • 44649172897 scopus 로고    scopus 로고
    • Efficient numerical solution of the LQR-problem for the heat equation
    • P. Benner, and J. Saak Efficient numerical solution of the LQR-problem for the heat equation Proc. Appl. Math. Mech. 4 1 2004 648 649
    • (2004) Proc. Appl. Math. Mech. , vol.4 , Issue.1 , pp. 648-649
    • Benner, P.1    Saak, J.2
  • 12
    • 33646471733 scopus 로고    scopus 로고
    • Benchmark examples for model reduction of linear time-invariant dynamical systems
    • Y. Chahlaoui, and P. Van Dooren Benchmark examples for model reduction of linear time-invariant dynamical systems Dimens. Reduct. Large-Scale Syst. 45 2005 381 395
    • (2005) Dimens. Reduct. Large-Scale Syst. , vol.45 , pp. 381-395
    • Chahlaoui, Y.1    Van Dooren, P.2
  • 13
    • 81555222620 scopus 로고    scopus 로고
    • Analysis of the rational Krylov subspace and ADI methods for solving the Lyapunov equation
    • V. Druskin, L. Knizhnerman, and V. Simoncini Analysis of the rational Krylov subspace and ADI methods for solving the Lyapunov equation SIAM J. Numer. Anal. 49 5 2011 1875 1898
    • (2011) SIAM J. Numer. Anal. , vol.49 , Issue.5 , pp. 1875-1898
    • Druskin, V.1    Knizhnerman, L.2    Simoncini, V.3
  • 14
    • 0036254232 scopus 로고    scopus 로고
    • Block Krylov subspace methods for solving large Sylvester equations
    • A. El Guennouni, K. Jbilou, and A.J. Riquet Block Krylov subspace methods for solving large Sylvester equations Numer. Algorithms 29 1 2002 75 96
    • (2002) Numer. Algorithms , vol.29 , Issue.1 , pp. 75-96
    • El Guennouni, A.1    Jbilou, K.2    Riquet, A.J.3
  • 15
    • 84870060561 scopus 로고    scopus 로고
    • 2-optimal interpolation: New properties and applications
    • Pittsburgh, PA, July
    • H2-optimal interpolation: New properties and applications, Talk given at the 2010 SIAM Annual Meeting, Pittsburgh, PA, July 2010.
    • (2010) Talk Given at the 2010 SIAM Annual Meeting
    • Flagg, G.M.1
  • 17
    • 84865039095 scopus 로고    scopus 로고
    • Structure-preserving tangential interpolation for model reduction of port-Hamiltonian systems
    • S. Gugercin, R.V. Polyuga, C.A. Beattie, and A. van der Schaft Structure-preserving tangential interpolation for model reduction of port-Hamiltonian systems Automatica 48 9 2012 1963 1974 arXiv:1101.3485v2
    • (2012) Automatica , vol.48 , Issue.9 , pp. 1963-1974
    • Gugercin, S.1    Polyuga, R.V.2    Beattie, C.A.3    Van Der Schaft, A.4
  • 18
    • 0037276767 scopus 로고    scopus 로고
    • A modified low-rank Smith method for large-scale Lyapunov equations
    • S. Gugercin, D.C. Sorensen, and A.C. Antoulas A modified low-rank Smith method for large-scale Lyapunov equations Numer. Algorithms 32 1 2003 27 55
    • (2003) Numer. Algorithms , vol.32 , Issue.1 , pp. 27-55
    • Gugercin, S.1    Sorensen, D.C.2    Antoulas, A.C.3
  • 19
    • 55549146123 scopus 로고    scopus 로고
    • Balanced truncation model reduction for a class of descriptor systems with application to the Oseen equations
    • M. Heinkenschloss, D.C. Sorensen, and K. Sun Balanced truncation model reduction for a class of descriptor systems with application to the Oseen equations SIAM J. Sci. Comput. 30 2008 1038
    • (2008) SIAM J. Sci. Comput. , vol.30 , pp. 1038
    • Heinkenschloss, M.1    Sorensen, D.C.2    Sun, K.3
  • 20
    • 38249011246 scopus 로고
    • Krylov-subspace methods for the Sylvester equation
    • D.Y. Hu, and L. Reichel Krylov-subspace methods for the Sylvester equation Linear Algebra Appl. 172 1992 283 313
    • (1992) Linear Algebra Appl. , vol.172 , pp. 283-313
    • Hu, D.Y.1    Reichel, L.2
  • 21
    • 0022188129 scopus 로고
    • The optimal projection equations for model reduction and the relationships among the methods of Wilson, Skelton, and Moore
    • D. Hyland, and D. Bernstein The optimal projection equations for model reduction and the relationships among the methods of Wilson, Skelton, and Moore IEEE Trans. Automat. Control 30 12 1985 1201 1211
    • (1985) IEEE Trans. Automat. Control , vol.30 , Issue.12 , pp. 1201-1211
    • Hyland, D.1    Bernstein, D.2
  • 22
    • 0028377922 scopus 로고
    • Krylov subspace methods for solving large Lyapunov equations
    • I.M. Jaimoukha, and E.M. Kasenally Krylov subspace methods for solving large Lyapunov equations SIAM J. Numer. Anal. 1994 227 251
    • (1994) SIAM J. Numer. Anal. , pp. 227-251
    • Jaimoukha, I.M.1    Kasenally, E.M.2
  • 23
    • 33744937558 scopus 로고    scopus 로고
    • Low rank approximate solutions to large Sylvester matrix equations
    • K. Jbilou Low rank approximate solutions to large Sylvester matrix equations Appl. Math. Comput. 177 1 2006 365 376
    • (2006) Appl. Math. Comput. , vol.177 , Issue.1 , pp. 365-376
    • Jbilou, K.1
  • 24
    • 0037287244 scopus 로고    scopus 로고
    • Low rank solution of Lyapunov equations
    • J.R. Li, and J. White Low rank solution of Lyapunov equations SIAM J. Matrix Anal. Appl. 24 1 2002 260 280
    • (2002) SIAM J. Matrix Anal. Appl. , vol.24 , Issue.1 , pp. 260-280
    • Li, J.R.1    White, J.2
  • 25
    • 11344287684 scopus 로고    scopus 로고
    • Low-rank solution of Lyapunov equations
    • J.R. Li, and J. White Low-rank solution of Lyapunov equations SIAM Rev. 46 2004 693 713
    • (2004) SIAM Rev. , vol.46 , pp. 693-713
    • Li, J.R.1    White, J.2
  • 27
    • 0002058827 scopus 로고
    • The numerical solution of parabolic and elliptic differential equations
    • D.W. Peaceman, and H.H. Rachford The numerical solution of parabolic and elliptic differential equations J. Soc. Ind. Appl. Math. 3 1 1955 28 41
    • (1955) J. Soc. Ind. Appl. Math. , vol.3 , Issue.1 , pp. 28-41
    • Peaceman, D.W.1    Rachford, H.H.2
  • 28
    • 0033295674 scopus 로고    scopus 로고
    • A cyclic low rank Smith method for large sparse Lyapunov equations
    • T. Penzl A cyclic low rank Smith method for large sparse Lyapunov equations SIAM J. Sci. Comput. 21 4 2000 1401 1418
    • (2000) SIAM J. Sci. Comput. , vol.21 , Issue.4 , pp. 1401-1418
    • Penzl, T.1
  • 30
    • 44649084929 scopus 로고    scopus 로고
    • A new iterative method for solving large-scale Lyapunov matrix equations
    • V. Simoncini A new iterative method for solving large-scale Lyapunov matrix equations SIAM J. Sci. Comput. 29 3 2008 1268 1288
    • (2008) SIAM J. Sci. Comput. , vol.29 , Issue.3 , pp. 1268-1288
    • Simoncini, V.1
  • 31
    • 31244437503 scopus 로고    scopus 로고
    • The Sylvester equation and approximate balanced reduction
    • D.C. Sorensen, and A.C. Antoulas The Sylvester equation and approximate balanced reduction Linear Algebra Appl. 351 2002 671 700
    • (2002) Linear Algebra Appl. , vol.351 , pp. 671-700
    • Sorensen, D.C.1    Antoulas, A.C.2
  • 33
    • 0026239062 scopus 로고
    • Optimal alternating direction implicit parameters for nonsymmetric systems of linear equations
    • G. Starke Optimal alternating direction implicit parameters for nonsymmetric systems of linear equations SIAM J. Numer. Anal. 28 5 1991 1431 1445
    • (1991) SIAM J. Numer. Anal. , vol.28 , Issue.5 , pp. 1431-1445
    • Starke, G.1
  • 34
    • 38249001860 scopus 로고
    • Fejer-Walsh points for rational functions and their use in the ADI iterative method
    • G. Starke Fejer-Walsh points for rational functions and their use in the ADI iterative method J. Comput. Appl. Math. 46 1-2 1993 129 141
    • (1993) J. Comput. Appl. Math. , vol.46 , Issue.12 , pp. 129-141
    • Starke, G.1
  • 35
    • 81055156814 scopus 로고    scopus 로고
    • Krylov subspace methods for projected Lyapunov equations
    • T. Stykel, and V. Simoncini Krylov subspace methods for projected Lyapunov equations Appl. Numer. Math. 62 1 2012 35 50
    • (2012) Appl. Numer. Math. , vol.62 , Issue.1 , pp. 35-50
    • Stykel, T.1    Simoncini, V.2
  • 36
    • 70349735245 scopus 로고    scopus 로고
    • On the ADI method for Sylvester equations
    • University of Texas at Arlington
    • N. Truhar, R.C. Li, On the ADI method for Sylvester equations, Technical Report 2008-02, Department of Mathematics, University of Texas at Arlington, 2008, available at http://www.uta.edu/math/preprint/rep200802.pdf.
    • (2008) Technical Report 2008-02, Department of Mathematics
    • Truhar, N.1    Li, R.C.2
  • 37
    • 0029692981 scopus 로고    scopus 로고
    • Mosaic-skeleton approximations
    • E. Tyrtyshnikov Mosaic-skeleton approximations Calcolo 33 1 1996 47 57
    • (1996) Calcolo , vol.33 , Issue.1 , pp. 47-57
    • Tyrtyshnikov, E.1
  • 39
    • 0005653922 scopus 로고
    • Extended application of alternating direction implicit iteration model problem theory
    • E.L. Wachspress Extended application of alternating direction implicit iteration model problem theory J. Soc. Ind. Appl. Math. 11 4 1963 994 1016
    • (1963) J. Soc. Ind. Appl. Math. , vol.11 , Issue.4 , pp. 994-1016
    • Wachspress, E.L.1
  • 40
    • 38249030580 scopus 로고
    • Iterative solution of the Lyapunov matrix equation
    • E.L. Wachspress Iterative solution of the Lyapunov matrix equation Appl. Math. Lett. 107 1988 87 90
    • (1988) Appl. Math. Lett. , vol.107 , pp. 87-90
    • Wachspress, E.L.1
  • 41
    • 38249031410 scopus 로고
    • The ADI minimax problem for complex spectra
    • E.L. Wachspress The ADI minimax problem for complex spectra Appl. Math. Lett. 1 3 1988 311 314
    • (1988) Appl. Math. Lett. , vol.1 , Issue.3 , pp. 311-314
    • Wachspress, E.L.1
  • 42
    • 40749144925 scopus 로고    scopus 로고
    • Trail to a Lyapunov equation solver
    • E.L. Wachspress Trail to a Lyapunov equation solver Comput. Math. Appl. 55 8 2008 1653 1659
    • (2008) Comput. Math. Appl. , vol.55 , Issue.8 , pp. 1653-1659
    • Wachspress, E.L.1
  • 43
    • 0014923452 scopus 로고
    • Optimum solution of model-reduction problem
    • D.A. Wilson Optimum solution of model-reduction problem Proc. IEE 117 6 1970 1161 1165.
    • (1970) Proc. IEE , vol.117 , Issue.6 , pp. 1161-1165
    • Wilson, D.A.1


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