메뉴 건너뛰기




Volumn 436, Issue 10, 2012, Pages 3883-3903

On convergence of Krylov subspace approximations of time-invariant self-adjoint dynamical systems

Author keywords

Dispersive media; Dynamical system; Exponential integrators; Fractional order equations; Krylov subspace; Matrix exponential; Model reduction; Nonlinear spectrum; Numerical range; Rational approximation; Structure preserving; Time domain Maxwell's system

Indexed keywords

DISPERSIVE MEDIA; EXPONENTIAL INTEGRATORS; FRACTIONAL ORDER; KRYLOV SUBSPACE; MATRIX EXPONENTIAL; MODEL REDUCTION; NONLINEAR SPECTRUM; NUMERICAL RANGE; RATIONAL APPROXIMATIONS; STRUCTURE PRESERVING; TIME DOMAIN;

EID: 84858800367     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2011.02.039     Document Type: Article
Times cited : (17)

References (47)
  • 2
    • 25444467698 scopus 로고    scopus 로고
    • Dimension reduction of large-scale second-order dynamical systems via a second-order arnoldi method
    • DOI 10.1137/040605552
    • Z. Bai, and Y. Su Dimension reduction of second-order dynamical systems via a second-order Arnoldi method SIAM J. Sci. Comput. 26 2005 1692 1709 (Pubitemid 41360310)
    • (2005) SIAM Journal of Scientific Computing , vol.26 , Issue.5 , pp. 1692-1709
    • Bai, Z.1    Yangfeng, S.U.2
  • 3
    • 22944474654 scopus 로고    scopus 로고
    • Soar: A second-order arnoldi method for the solution of the quadratic eigenvalue problem
    • DOI 10.1137/S0895479803438523
    • Z. Bai, and Y. Su Soar A second-order Arnoldi method for the solution of the quadratic eigenvalue problem SIAM J. Matrix Anal. Appl. 26 2005 640 659 (Pubitemid 41049837)
    • (2005) SIAM Journal on Matrix Analysis and Applications , vol.26 , Issue.3 , pp. 640-659
    • Bai, Z.1    Su, Y.2
  • 4
    • 0034548677 scopus 로고    scopus 로고
    • Optimal rational functions for the generalized Zolotarev problem in the complex plane
    • PII S0036142999360688
    • B. Le Bailly, and J. Thiran Optimal rational functions for the generalized Zolotarev problem in the complex plane SIAM J. Numer. Anal. 38 2000 1409 1424 (Pubitemid 33778950)
    • (2000) SIAM Journal on Numerical Analysis , vol.38 , Issue.5 , pp. 1409-1424
    • Le Bailly, B.1    Thiran, J.P.2
  • 6
    • 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 3849 3883
    • (2009) SIAM J. Numer. Anal. , vol.47 , pp. 3849-3883
    • Beckermann, B.1    Reichel, L.2
  • 7
    • 58249141852 scopus 로고    scopus 로고
    • Interpolatory projection methods for structure-preserving model reduction
    • C. Beattie, and S. Gugercin Interpolatory projection methods for structure-preserving model reduction Systems Control Lett. 58 2009 223 225
    • (2009) Systems Control Lett. , vol.58 , pp. 223-225
    • Beattie, C.1    Gugercin, S.2
  • 8
    • 84857259846 scopus 로고
    • Dispersion and absorption in dielectrics
    • K. Cole, and R. Cole Dispersion and absorption in dielectrics J. Chem. Phys. 6 1941 42 52
    • (1941) J. Chem. Phys. , vol.6 , pp. 42-52
    • Cole, K.1    Cole, R.2
  • 9
    • 33748049827 scopus 로고    scopus 로고
    • Electrical-prospecting method for hydrocarbon search using the induced-polarization effect
    • S. Davydycheva, N. Rykhlinski, and P. Legeido Electrical-prospecting method for hydrocarbon search using the induced-polarization effect Geophysics 71 2006 G179 G189
    • (2006) Geophysics , vol.71
    • Davydycheva, S.1    Rykhlinski, N.2    Legeido, P.3
  • 10
    • 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 3760 3780
    • (2009) SIAM J. Sci. Comput. , vol.31 , pp. 3760-3780
    • Druskin, V.1    Knizhnerman, L.2    Zaslavsky, M.3
  • 11
    • 0000075482 scopus 로고
    • A spectral semi-discrete method for the numerical solution of three-dimensional non-stationary electrical prospecting problems
    • (in Russian, translated into English)
    • V. Druskin, and L. Knizhnerman A spectral semi-discrete method for the numerical solution of three-dimensional non-stationary electrical prospecting problems Izv. AN USSR, Ser. Phys. Solid Earth 8 1988 63 74 (in Russian, translated into English)
    • (1988) Izv. AN USSR, Ser. Phys. Solid Earth , vol.8 , pp. 63-74
    • Druskin, V.1    Knizhnerman, L.2
  • 12
    • 0000446481 scopus 로고
    • Two polynomial methods of calculating functions of symmetric matrices
    • V. Druskin, and L. Knizhnerman Two polynomial methods of calculating functions of symmetric matrices USSR Comput. Math. Math. Phys. 29 1989 112 121
    • (1989) USSR Comput. Math. Math. Phys. , vol.29 , pp. 112-121
    • Druskin, V.1    Knizhnerman, L.2
  • 13
    • 78149325330 scopus 로고    scopus 로고
    • On adaptive choice of shifts in rational Krylov subspace reduction of evolutionary problems
    • V. Druskin, C. Lieberman, and M. Zaslavsky On adaptive choice of shifts in rational Krylov subspace reduction of evolutionary problems SIAM J. Sci. Comput. 32 2010 2485 2496
    • (2010) SIAM J. Sci. Comput. , vol.32 , pp. 2485-2496
    • Druskin, V.1    Lieberman, C.2    Zaslavsky, M.3
  • 14
    • 16244364781 scopus 로고    scopus 로고
    • SPRIM: Structure-preserving reduced-order interconnect macromodeling
    • 1D.2, ICCAD-2004 - IEEE/ACM International Conference on Computer-Aided Design, Digest of Technical Papers
    • R. Freund SPRIM: structure-preserving reduced-order interconnect macromodeling Technical Digest of the 2004 IEEE/ACM International Conference on Computer-Aided Design, Los Alamitos 2004 IEEE Computer Society Press California 80 87 (Pubitemid 40449217)
    • (2004) IEEE/ACM International Conference on Computer-Aided Design, Digest of Technical Papers, ICCAD , pp. 80-87
    • Freund, R.W.1
  • 15
    • 28144462350 scopus 로고    scopus 로고
    • Padé-type model reduction of second order and high order dynamical systems
    • P. Benner, V. Mehrmann, D.C. Sorensen, Lecture Notes in Computational Science and Engineering Springer-Verlarg Berlin, Heidelberg
    • R. Freund Padé-type model reduction of second order and high order dynamical systems P. Benner, V. Mehrmann, D.C. Sorensen, Dimension Reduction of Large Scale Systems Lecture Notes in Computational Science and Engineering vol. 45 2005 Springer-Verlarg Berlin, Heidelberg 191 223
    • (2005) Dimension Reduction of Large Scale Systems , vol.45 VOL. , pp. 191-223
    • Freund, R.1
  • 16
    • 51349104199 scopus 로고    scopus 로고
    • On Padé-type model order reduction of J-Hermitian linear dynamical systems
    • R. Freund On Padé-type model order reduction of J-Hermitian linear dynamical systems Linear Algebra Appl. 429 2008 2451 2464
    • (2008) Linear Algebra Appl. , vol.429 , pp. 2451-2464
    • Freund, R.1
  • 18
    • 0000269389 scopus 로고
    • Efficient solution of parabolic equations by Krylov approximation method
    • E. Gallopulos, and Y. Saad Efficient solution of parabolic equations by Krylov approximation method SIAM J. Sci. Stat. Comput. 13 1992 1236 1264
    • (1992) SIAM J. Sci. Stat. Comput. , vol.13 , pp. 1236-1264
    • Gallopulos, E.1    Saad, Y.2
  • 21
    • 27844482948 scopus 로고    scopus 로고
    • Numerical solution of parameter-dependent linear systems
    • DOI 10.1002/nla.442
    • G.-D. Gu, and V. Simoncini Numerical solution of parameter-dependent linear systems Numer. Linear Algebra Appl. 12 2005 923 940 (Pubitemid 41639472)
    • (2005) Numerical Linear Algebra with Applications , vol.12 , Issue.9 , pp. 923-940
    • Gu, G.-D.1    Simoncini, V.2
  • 23
    • 0040334472 scopus 로고
    • Numerical determination of the field of values of a general complex matrix
    • C. Johnson Numerical determination of the field of values of a general complex matrix SIAM J. Numer. Anal. 5 1978 595 602
    • (1978) SIAM J. Numer. Anal. , vol.5 , pp. 595-602
    • Johnson, C.1
  • 24
    • 0347799731 scopus 로고    scopus 로고
    • On Krylov Subspace Approximations to the Matrix Exponential Operator
    • M. Hochbruck, and C. Lubich On Krylov subspace approximations to the matrix exponential operator SIAM J. Numer. Anal. 34 1997 1911 1925 (Pubitemid 127463577)
    • (1997) SIAM Journal on Numerical Analysis , vol.34 , Issue.5 , pp. 1911-1925
    • Hochbruck, M.1    Lubich, C.2
  • 26
    • 0002658611 scopus 로고
    • Computation of functions of unsymmetric matrices by means of the Arnoldi method
    • (in Russian, translated into English)
    • L. Knizhnerman Computation of functions of unsymmetric matrices by means of the Arnoldi method J. Comput. Math. Math. Phys. 31 1991 5 16 (in Russian, translated into English)
    • (1991) J. Comput. Math. Math. Phys. , vol.31 , pp. 5-16
    • Knizhnerman, L.1
  • 27
    • 84858791993 scopus 로고
    • The numerical solution of Cauchy's problem for the Laplace equation by means of decomposition into Fourier-Chebyshev series
    • (in Russian, translated into English)
    • L. Knizhnerman The numerical solution of Cauchy's problem for the Laplace equation by means of decomposition into Fourier-Chebyshev series Izv. AN USSR, Ser. Phys. Solid Earth 10 1984 76 81 (in Russian, translated into English)
    • (1984) Izv. AN USSR, Ser. Phys. Solid Earth , vol.10 , pp. 76-81
    • Knizhnerman, L.1
  • 28
    • 77951523457 scopus 로고    scopus 로고
    • On optimal convergence rate of the rational Krylov subspace reduction for electromagnetic problems in unbounded domains
    • L. Knizhnerman, V. Druskin, and M. Zaslavsky On optimal convergence rate of the rational Krylov subspace reduction for electromagnetic problems in unbounded domains SIAM J. Numer. Anal. 47 2009 953 971
    • (2009) SIAM J. Numer. Anal. , vol.47 , pp. 953-971
    • Knizhnerman, L.1    Druskin, V.2    Zaslavsky, M.3
  • 29
  • 30
    • 81555222614 scopus 로고    scopus 로고
    • On the convergence of the Krylov subspace methods for matrix Mittag-Leffler functions
    • submitted for publication
    • I. Moret, P. Novati, On the convergence of the Krylov subspace methods for matrix Mittag-Leffler functions, SIAM J. Numer. Anal., submitted for publication.
    • SIAM J. Numer. Anal.
    • Moret, I.1    Novati, P.2
  • 32
    • 34547851565 scopus 로고    scopus 로고
    • Lower bounds for separable approximations of the Hilbert kernel
    • (in Russian, translated into English)
    • I. Oseledets Lower bounds for separable approximations of the Hilbert kernel Math. Digest (Matem. Sb.) 198 2007 425 432 (in Russian, translated into English)
    • (2007) Math. Digest (Matem. Sb.) , vol.198 , pp. 425-432
    • Oseledets, I.1
  • 35
    • 0001409002 scopus 로고
    • The rational Krylov algorithm for nonsymmetric eigenvalue problems. III: Complex shifts for real matrices
    • A. Ruhe The rational Krylov algorithm for nonsymmetric eigenvalue problems. III: Complex shifts for real matrices BIT 34 1994 65 176
    • (1994) BIT , vol.34 , pp. 65-176
    • Ruhe, A.1
  • 36
    • 0026818185 scopus 로고
    • Analysis of some Krylov subspace approximations to the matrix exponential operator
    • Y. Saad Analysis of some Krylov subspace approximations to the matrix exponential operator SIAM J. Numer. Anal. 29 1992 209 228
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 209-228
    • Saad, Y.1
  • 39
    • 0026123113 scopus 로고
    • Model reduction and control of flexible structures using Krylov vectors
    • T.-J. Su, and R. Craig Jr. Model reduction and control of flexible structures using Krylov vectors J. Guid. Control Dyn. 14 1991 260 267
    • (1991) J. Guid. Control Dyn. , vol.14 , pp. 260-267
    • Su, T.-J.1    Craig Jr., R.2
  • 41
    • 0029692981 scopus 로고    scopus 로고
    • Mosaic-skeleton approximations
    • E. Tyrtyshnikov Mosaic-skeleton approximations Calcolo 33 1996 47 57
    • (1996) Calcolo , vol.33 , pp. 47-57
    • Tyrtyshnikov, E.1
  • 42
    • 0001646445 scopus 로고
    • An iterative solution method for solving f (A) x = b using Krylov subspace information obtained for the symmetric positive definite matrix
    • H. Van der Vorst An iterative solution method for solving f (A) x = b using Krylov subspace information obtained for the symmetric positive definite matrix J. Comput. Appl. Math. 18 1987 249 263
    • (1987) J. Comput. Appl. Math. , vol.18 , pp. 249-263
    • Van Der Vorst, H.1
  • 43
    • 4444266799 scopus 로고    scopus 로고
    • An Arnoldi method for nonlinear eigenvalue problems
    • DOI 10.1023/B:BITN.0000039424.56697.8b
    • H. Voss An Arnoldi method for nonlinear eigenvalue problems BIT 44 2004 387 401 (Pubitemid 39187343)
    • (2004) BIT Numerical Mathematics , vol.44 , Issue.2 , pp. 387-401
    • Voss, H.1
  • 44
    • 70449111471 scopus 로고    scopus 로고
    • A minmax principle for nonlinear eigenproblems depending continuously on the eigenparameter
    • H. Voss A minmax principle for nonlinear eigenproblems depending continuously on the eigenparameter Numer. Linear Algebra Appl. 16 2009 899 913
    • (2009) Numer. Linear Algebra Appl. , vol.16 , pp. 899-913
    • Voss, H.1
  • 45
    • 34548162562 scopus 로고    scopus 로고
    • Parabolic and hyperbolic contours for computing the Bromwich integral
    • J. Weideman, and L. Trefethen Parabolic and hyperbolic contours for computing the Bromwich integral Math. Comp. 76 2007 1341 1356
    • (2007) Math. Comp. , vol.76 , pp. 1341-1356
    • Weideman, J.1    Trefethen, L.2
  • 46
    • 33845419187 scopus 로고    scopus 로고
    • Finite-difference solution of the three-dimensional electromagnetic problem using divergence-free preconditioners
    • DOI 10.1190/1.2370372
    • M. Zaslavsky, S. Davydycheva, V. Druskin, A. Abubakar, T. Habashy, L. Knizhnerman, Finite-difference solution of the 3D electromagnetic problem using divergence-free preconditioners, in: Proceedings of SEG Annual Meeting, New Orleans, 2006, pp. 775-778. (Pubitemid 44889781)
    • (2006) SEG Technical Program Expanded Abstracts , vol.25 , Issue.1 , pp. 775-778
    • Zaslavsk, M.1    Davydycheva, S.2    Druskin, V.3    Abubakar, A.4    Habashy, T.5    Knizhnerman, L.6
  • 47
    • 77951542206 scopus 로고    scopus 로고
    • Solution of time-convolutionary Maxwell's equations using parameter-dependent Krylov subspace reduction
    • M. Zaslavsky, and V. Druskin Solution of time-convolutionary Maxwell's equations using parameter-dependent Krylov subspace reduction JCP 229 2010 4831 4839
    • (2010) JCP , vol.229 , pp. 4831-4839
    • Zaslavsky, M.1    Druskin, V.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.