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Volumn 49, Issue 6, 2011, Pages 2430-2450

An error analysis for rational galerkin projection applied to the sylvester equation

Author keywords

ADI; Galerkin projection; Lyapunov equation; Rational Krylov spaces; Sylvester equation

Indexed keywords

ADI; GALERKIN PROJECTIONS; LYAPUNOV EQUATION; RATIONAL KRYLOV SPACES; SYLVESTER EQUATION;

EID: 84856024767     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/110824590     Document Type: Article
Times cited : (49)

References (36)
  • 1
    • 34047199854 scopus 로고    scopus 로고
    • Approximation of large-scale dynamical systems
    • SIAM, Philadelphia
    • A. C. Antoulas, Approximation of Large-Scale Dynamical Systems, Adv. Des. Control, SIAM, Philadelphia, 2005.
    • (2005) Adv. Des. Control
    • Antoulas, A.C.1
  • 2
    • 70349741655 scopus 로고    scopus 로고
    • Cross-Gramian based model reduction for data-sparse systems
    • U. Baur and P. Benner, Cross-Gramian based model reduction for data-sparse systems, Electron. Trans. Numer. Anal., 31 (2008), pp. 256-270.
    • (2008) Electron. Trans. Numer. Anal. , vol.31 , pp. 256-270
    • Baur, U.1    Benner, P.2
  • 3
    • 19544371885 scopus 로고    scopus 로고
    • Image numérique, GMRES et polynômes de Faber
    • DOI 10.1016/j.crma.2005.04.027, PII S1631073X05001755
    • B. Beckermann, Image numérique, GMRES et polynômes de Faber, C. R. Acad. Sci. Paris, Ser. I, 340 (2005), pp. 855-860. (Pubitemid 40735387)
    • (2005) Comptes Rendus Mathematique , vol.340 , Issue.11 , pp. 855-860
    • Beckermann, B.1
  • 4
    • 77957300827 scopus 로고    scopus 로고
    • Extremal rational functions on symmetric discrete sets and superlinear convergence of the ADI method
    • B. Beckermann and A. Gryson, Extremal rational functions on symmetric discrete sets and superlinear convergence of the ADI method, Constr. Approx., 32 (2010), pp. 393-428.
    • (2010) Constr. Approx. , vol.32 , pp. 393-428
    • Beckermann, B.1    Gryson, A.2
  • 5
    • 84856037108 scopus 로고    scopus 로고
    • Superlinear convergence of the polynomial and rational Arnoldi methods for matrix functions
    • to appear
    • B. Beckermann and S. Güttel, Superlinear convergence of the polynomial and rational Arnoldi methods for matrix functions, Numer. Math., to appear.
    • Numer. Math.
    • Beckermann, B.1    Güttel, S.2
  • 7
    • 0035733975 scopus 로고    scopus 로고
    • Superlinear convergence of Conjugate gradients
    • B. Beckermann and A. B. J. Kuijlaars, Superlinear convergence of Conjugate gradients, SIAM J. Numer. Anal., 39 (2001), pp. 300-329.
    • (2001) SIAM J. Numer. Anal. , vol.39 , pp. 300-329
    • Beckermann, B.1    Kuijlaars, A.B.J.2
  • 8
    • 84904192266 scopus 로고    scopus 로고
    • Error estimation and evaluation of matrix functions via the Faber transform
    • B. Beckermann and L. Reichel, Error estimation and evaluation of matrix functions via the Faber transform, SIAM J. Numer. Anal., 47 (2009), pp. 3849-3883.
    • (2009) SIAM J. Numer. Anal. , vol.47 , pp. 3849-3883
    • Beckermann, B.1    Reichel, L.2
  • 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 (2009), pp. 1035-1045.
    • (2009) J. Comput. Appl. Math. , vol.233 , pp. 1035-1045
    • Benner, P.1    Li, R.-C.2    Truhar, N.3
  • 11
    • 84931151127 scopus 로고
    • Implicit alternating direction methods
    • G. Birkhoff and R. S. Varga, Implicit alternating direction methods, Trans. Amer. Math. Soc., 92 (1959), pp. 13-24.
    • (1959) Trans. Amer. Math. Soc. , vol.92 , pp. 13-24
    • Birkhoff, G.1    Varga, R.S.2
  • 12
    • 0030532987 scopus 로고    scopus 로고
    • Application of ADI iterative methods to the restoration of noisy images
    • D. Calvetti and L. Reichel, Application of ADI iterative methods to the restoration of noisy images, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 165-186.
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , pp. 165-186
    • Calvetti, D.1    Reichel, L.2
  • 13
    • 33846829563 scopus 로고    scopus 로고
    • Numerical range and functional calculus in Hilbert space
    • M. Crouzeix, Numerical range and functional calculus in Hilbert space, J. Funct. Anal., 244 (2007), pp. 668-690.
    • (2007) J. Funct. Anal. , vol.244 , pp. 668-690
    • Crouzeix, M.1
  • 15
    • 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 (2011), pp. 1875-1898.
    • (2011) SIAM J. Numer. Anal. , vol.49 , pp. 1875-1898
    • Druskin, V.1    Knizhnerman, L.2    Simoncini, V.3
  • 16
    • 77951568661 scopus 로고    scopus 로고
    • Solution of large scale evolutionary problems using rational Krylov subspaces with optimized shifts
    • V. Druskin, L. Knizhnerman, and M. Zaslavsky, Solution of large scale evolutionary problems using rational Krylov subspaces with optimized shifts, SIAM J. Sci. Comput., 31 (2009), pp. 3760-3780.
    • (2009) SIAM J. Sci. Comput. , vol.31 , pp. 3760-3780
    • Druskin, V.1    Knizhnerman, L.2    Zaslavsky, M.3
  • 17
    • 79959705270 scopus 로고    scopus 로고
    • Adaptive rational Krylov subspaces for large-scale dynamical systems
    • V. Druskin and V. Simoncini, Adaptive rational Krylov subspaces for large-scale dynamical systems, Systems Control Lett., 60 (2011), pp. 546-560.
    • (2011) Systems Control Lett. , vol.60 , pp. 546-560
    • Druskin, V.1    Simoncini, V.2
  • 18
    • 84976797154 scopus 로고
    • Improving the efficiency of matrix operations in the numerical solution of stiff ordinary differential equations
    • W. H. Enright, Improving the efficiency of matrix operations in the numerical solution of stiff ordinary differential equations, ACM Trans. Math. Software, 4 (1978), pp. 127-136.
    • (1978) ACM Trans. Math. Software , vol.4 , pp. 127-136
    • Enright, W.H.1
  • 19
    • 21344460034 scopus 로고    scopus 로고
    • A rational Lanczos algorithm for model reduction
    • K. Gallivan, E. Grimme, and P. Van Dooren, A rational Lanczos algorithm for model reduction, Numer. Algorithms, 12 (1996), pp. 33-63. (Pubitemid 126725676)
    • (1996) Numerical Algorithms , vol.12 , Issue.1-2 , pp. 33-63
    • Gallivan, K.1    Grimme, E.2    Van Dooren, P.3
  • 20
    • 0004236492 scopus 로고    scopus 로고
    • 3rd ed., Johns Hopkins University Press, Baltimore, MD
    • G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed., Johns Hopkins University Press, Baltimore, MD, 1996.
    • (1996) Matrix Computations
    • Golub, G.H.1    Van Loan, C.F.2
  • 21
    • 0041023452 scopus 로고
    • Zolotarev problems connected with rational functions
    • A. A. Gonchar, Zolotarev problems connected with rational functions, Math. Digest (Matem. Sb.), 7 (1969), pp. 623-635.
    • (1969) Math. Digest (Matem. Sb. , vol.7 , pp. 623-635
    • Gonchar, A.A.1
  • 22
    • 0004067099 scopus 로고    scopus 로고
    • Ph.D. thesis, The University of Illinois at Urbana-Champaign, Champaign, IL
    • E. Grimme, Krylov Projection Methods for Model Reduction, Ph.D. thesis, The University of Illinois at Urbana-Champaign, Champaign, IL, 1997.
    • (1997) Krylov Projection Methods for Model Reduction
    • Grimme, E.1
  • 23
    • 56749147915 scopus 로고    scopus 로고
    • H2 model reduction for large-scale linear dynamical systems
    • S. Gugercin, A. C. Antoulas, and C. Beattie, H2 model reduction for large-scale linear dynamical systems, SIAM J. Matrix Anal. Appl., 30 (2008), pp. 609-638.
    • (2008) SIAM J. Matrix Anal. Appl. , vol.30 , pp. 609-638
    • Gugercin, S.1    Antoulas, A.C.2    Beattie, C.3
  • 24
    • 79958288318 scopus 로고    scopus 로고
    • Convergence analysis of the extended Krylov subspace method for the Lyapunov equation
    • L. Knizhnerman and V. Simoncini, Convergence analysis of the extended Krylov subspace method for the Lyapunov equation, Numer. Math., 118 (2011), pp. 567-586.
    • (2011) Numer. Math. , vol.118 , pp. 567-586
    • Knizhnerman, L.1    Simoncini, V.2
  • 25
    • 77956045829 scopus 로고    scopus 로고
    • Krylov subspace methods for linear systems with tensor product structure
    • D. Kressner and Ch. Tobler, Krylov subspace methods for linear systems with tensor product structure, SIAM J. Matrix Anal. Appl., 31 (2010), pp. 1688-1714.
    • (2010) SIAM J. Matrix Anal. Appl. , vol.31 , pp. 1688-1714
    • Kressner, D.1    Tobler, C.2
  • 27
    • 0002058827 scopus 로고
    • The numerical solution of elliptic and parabolic differential equations
    • D. W. Peaceman and H. H. Rachford, Jr., The numerical solution of elliptic and parabolic differential equations, J. Soc. Indust. Appl. Math., 3 (1955), pp. 28-41.
    • (1955) J. Soc. Indust. Appl. Math. , vol.3 , pp. 28-41
    • Peaceman, D.W.1    Rachford Jr., H.H.2
  • 28
    • 0001082478 scopus 로고    scopus 로고
    • Eigenvalue decay bounds for solutions of Lyapunov equations: The symmetric case
    • T. Penzl, Eigenvalue decay bounds for solutions of Lyapunov equations: The symmetric case, Systems Control Lett., 40 (2000), pp. 139-144.
    • (2000) Systems Control Lett. , vol.40 , pp. 139-144
    • Penzl, T.1
  • 29
    • 0000175612 scopus 로고
    • Numerical solution of large Lyapunov equations
    • M. A. Kaashoek, J. H. van Schuppen, and A. C. Ran, eds., Signal Processing, Scattering, Operator Theory, and Numerical Methods, Birkhäuser Boston, Boston
    • Y. Saad, Numerical solution of large Lyapunov equations, in Proceedings of the International Symposium MTNS-89, Vol. III, M. A. Kaashoek, J. H. van Schuppen, and A. C. Ran, eds., Signal Processing, Scattering, Operator Theory, and Numerical Methods, Birkhäuser Boston, Boston, 1990, pp. 503-511.
    • (1990) Proceedings of the International Symposium MTNS-89 , vol.3 , pp. 503-511
    • Saad, Y.1
  • 32
    • 60049085652 scopus 로고    scopus 로고
    • Convergence analysis of projection methods for the numerical solution of large Lyapunov equations
    • V. Simoncini and V. Druskin, Convergence analysis of projection methods for the numerical solution of large Lyapunov equations, SIAM J. Numer. Anal., 47 (2009), pp. 828-843.
    • (2009) SIAM J. Numer. Anal. , vol.47 , pp. 828-843
    • Simoncini, V.1    Druskin, V.2
  • 33
    • 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., 351/352 (2002), pp. 671-700.
    • (2002) Linear Algebra Appl. , vol.351-352 , pp. 671-700
    • Sorensen, D.C.1    Antoulas, A.C.2
  • 35
    • 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. Indust. Appl. Math., 11 (1963), pp. 994-1016.
    • (1963) J. Soc. Indust. Appl. Math. , vol.11 , pp. 994-1016
    • Wachspress, E.L.1
  • 36
    • 84856029226 scopus 로고
    • Solution of the generalized ADI minimax problem
    • (Proc. IFIP Congress, Edinburgh, Mathematics, Software, North-Holland, Amsterdam, 1969
    • E. L. Wachspress, Solution of the generalized ADI minimax problem, in Information Processing 68 (Proc. IFIP Congress, Edinburgh, 1968), Vol. 1: Mathematics, Software, North-Holland, Amsterdam, 1969, pp. 99-105.
    • (1968) Information Processing , vol.1 , pp. 99-105
    • Wachspress, E.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.