메뉴 건너뛰기




Volumn 32, Issue 5, 2010, Pages 2485-2496

On adaptive choice of shifts in rational krylov subspace reduction of evolutionary problems

Author keywords

Greedy algorithm; Matrix exponential; Matrix function; Model reduction; Rational approximation; Time domain Maxwell system

Indexed keywords

APPROXIMATION ALGORITHMS; FREQUENCY DOMAIN ANALYSIS; RATIONAL FUNCTIONS; SPECTRAL DENSITY;

EID: 78149325330     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/090774082     Document Type: Article
Times cited : (71)

References (20)
  • 1
    • 0001868848 scopus 로고
    • On interpolation by rational functions
    • T. Bagby, On interpolation by rational functions, Duke Math. J., 36 (1969), pp. 95-104.
    • (1969) Duke Math. J. , vol.36 , pp. 95-104
    • Bagby, T.1
  • 2
    • 0034548677 scopus 로고    scopus 로고
    • Optimal rational functions for the generalized Zolotarev problem in the complex plane
    • B. Le Bailly and J. Thiran, Optimal rational functions for the generalized Zolotarev problem in the complex plane, SIAM J. Numer. Anal., 38 (2000), pp. 1409-1424.
    • (2000) SIAM J. Numer. Anal. , vol.38 , pp. 1409-1424
    • Le Bailly, B.1    Thiran, J.2
  • 3
    • 84904192266 scopus 로고    scopus 로고
    • Error estimates and evaluation of matrix functions via the Faber transform
    • B. Beckermann and L. Reichel, Error estimates 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
  • 4
    • 55149091531 scopus 로고    scopus 로고
    • Model reduction for large-scale systems with high-dimensional parametric input space
    • T. Bui-Thanh, K. Willcox, and O. Ghattas, Model reduction for large-scale systems with high-dimensional parametric input space, SIAM J. Sci. Comput., 30 (2008), pp. 3270-3288.
    • (2008) SIAM J. Sci. Comput. , vol.30 , pp. 3270-3288
    • Bui-Thanh, T.1    Willcox, K.2    Ghattas, O.3
  • 5
    • 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
  • 6
    • 84858800367 scopus 로고    scopus 로고
    • On convergence of krylov subspace approximations of timeinvariant hermitian dynamical systems
    • to appear
    • V. Druskin and M. Zaslavsky, On convergence of Krylov subspace approximations of timeinvariant Hermitian dynamical systems, Linear Algebra Appl., to appear.
    • Linear Algebra Appl.
    • Druskin, V.1    Zaslavsky, M.2
  • 7
    • 33646928736 scopus 로고    scopus 로고
    • Preconditioning Lanczos approximations to the matrix exponential
    • J. van den Eshof and M. Hochbruck, Preconditioning Lanczos approximations to the matrix exponential, SIAM J. Sci. Comput., 27 (2006), pp. 1438-1457.
    • (2006) SIAM J. Sci. Comput. , vol.27 , pp. 1438-1457
    • Van Den Eshof, J.1    Hochbruck, M.2
  • 8
    • 13844273168 scopus 로고    scopus 로고
    • Model reduction methods based on Krylov subspaces
    • R. Freund, Model reduction methods based on Krylov subspaces, Acta Numer., 12 (2003), pp. 267-319.
    • (2003) Acta Numer. , vol.12 , pp. 267-319
    • Freund, R.1
  • 11
    • 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), pp. 953-971.
    • (2009) SIAM J. Numer. Anal. , vol.47 , pp. 953-971
    • Knizhnerman, L.1    Druskin, V.2    Zaslavsky, M.3
  • 12
    • 78149346176 scopus 로고
    • On Zolotarev problems in the alternating direction method. II
    • S. L. Sobolev, Novosibirsk, Nauka, Moscow, (in Russian)
    • V. Lebedev, On Zolotarev problems in the alternating direction method. II, in Trudy Semin. S. L. Sobolev, No.1, Novosibirsk, Nauka, Moscow, 1976, pp. 51-59 (in Russian).
    • (1976) Trudy Semin. , Issue.1 , pp. 51-59
    • Lebedev, V.1
  • 13
  • 14
    • 35048893715 scopus 로고    scopus 로고
    • RD-rational approximations of matrix exponential
    • I. Moret and P. Novati, RD-rational approximations of matrix exponential, BIT, 43 (2003), pp. 1-18.
    • (2003) BIT , vol.43 , pp. 1-18
    • Moret, I.1    Novati, P.2
  • 15
    • 34547851565 scopus 로고    scopus 로고
    • Lower bounds for separable approximations of the Hilbert kernel
    • (in Russian)
    • I. Oseledets, Lower bounds for separable approximations of the Hilbert kernel, Sb. Math., 198 (2007), pp. 425-432 (in Russian).
    • (2007) Sb. Math. , vol.198 , pp. 425-432
    • Oseledets, I.1
  • 16
    • 49749108595 scopus 로고    scopus 로고
    • Acceleration techniques for approximating the matrix exponential operator
    • M. Popolizio and V. Simoncini, Acceleration techniques for approximating the matrix exponential operator, SIAM J. Matrix Anal. Appl., 30 (2008), pp. 657-683.
    • (2008) SIAM J. Matrix Anal. Appl. , vol.30 , pp. 657-683
    • Popolizio, M.1    Simoncini, V.2
  • 17
    • 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), pp. 165-176.
    • (1994) BIT , vol.34 , pp. 165-176
    • Ruhe, A.1
  • 19
    • 0029692981 scopus 로고    scopus 로고
    • Mosaic-skeleton approximations
    • E. Tyrtyshnikov, Mosaic-skeleton approximations, Calcolo, 33 (1996), pp. 47-57.
    • (1996) Calcolo , vol.33 , pp. 47-57
    • Tyrtyshnikov, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.